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fe_raviart.C
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1// The libMesh Finite Element Library.
2// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
3
4// This library is free software; you can redistribute it and/or
5// modify it under the terms of the GNU Lesser General Public
6// License as published by the Free Software Foundation; either
7// version 2.1 of the License, or (at your option) any later version.
8
9// This library is distributed in the hope that it will be useful,
10// but WITHOUT ANY WARRANTY; without even the implied warranty of
11// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12// Lesser General Public License for more details.
13
14// You should have received a copy of the GNU Lesser General Public
15// License along with this library; if not, write to the Free Software
16// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17
18
19
20// Local includes
21#include "libmesh/dof_map.h"
22#include "libmesh/elem.h"
23#include "libmesh/enum_to_string.h"
24#include "libmesh/fe.h"
25#include "libmesh/fe_interface.h"
26#include "libmesh/fe_macro.h"
27#include "libmesh/tensor_value.h"
28
29
30namespace libMesh
31{
32
33
34LIBMESH_DEFAULT_VECTORIZED_FE(0,RAVIART_THOMAS)
35LIBMESH_DEFAULT_VECTORIZED_FE(1,RAVIART_THOMAS)
36LIBMESH_DEFAULT_VECTORIZED_FE(2,RAVIART_THOMAS)
37LIBMESH_DEFAULT_VECTORIZED_FE(3,RAVIART_THOMAS)
38LIBMESH_DEFAULT_VECTORIZED_FE(0,L2_RAVIART_THOMAS)
39LIBMESH_DEFAULT_VECTORIZED_FE(1,L2_RAVIART_THOMAS)
40LIBMESH_DEFAULT_VECTORIZED_FE(2,L2_RAVIART_THOMAS)
41LIBMESH_DEFAULT_VECTORIZED_FE(3,L2_RAVIART_THOMAS)
42
43
44// Anonymous namespace for local helper functions
45namespace {
46void raviart_thomas_nodal_soln(const Elem * elem,
47 const Order order,
48 const std::vector<Number> & elem_soln,
49 const int dim,
50 const int vdim,
51 std::vector<Number> & nodal_soln,
52 const bool add_p_level)
53{
54 const unsigned int n_nodes = elem->n_nodes();
55 const ElemType elem_type = elem->type();
56
57 const Order totalorder = order + add_p_level*elem->p_level();
58
59 nodal_soln.resize(n_nodes*vdim);
60
61 FEType p_refined_fe_type(totalorder, RAVIART_THOMAS);
62
63 if (elem_type != TRI6 && elem_type != TRI7 &&
64 elem_type != QUAD8 && elem_type != QUAD9 &&
65 elem_type != TET14 && elem_type != HEX27)
66 libmesh_error_msg("ERROR: Invalid ElemType " << Utility::enum_to_string(elem_type) << " selected for RAVIART_THOMAS FE family!");
67
68 const unsigned int n_sf = FEInterface::n_shape_functions(p_refined_fe_type, elem, false);
69
70 std::vector<Point> refspace_nodes;
71 FEVectorBase::get_refspace_nodes(elem_type,refspace_nodes);
72 libmesh_assert_equal_to (refspace_nodes.size(), n_nodes);
73 libmesh_assert_equal_to (elem_soln.size(), n_sf);
74
75 // Need to create new fe object so the shape function has the FETransformation
76 // applied to it.
77 std::unique_ptr<FEVectorBase> vis_fe = FEVectorBase::build(dim, p_refined_fe_type);
78
79 const std::vector<std::vector<RealGradient>> & vis_phi = vis_fe->get_phi();
80
81 vis_fe->reinit(elem,&refspace_nodes);
82
83 // Zero before summation
84 std::fill(nodal_soln.begin(), nodal_soln.end(), 0);
85
86 for (unsigned int n = 0; n < n_nodes; n++)
87 // u = Sum (u_i phi_i)
88 for (unsigned int i=0; i<n_sf; i++)
89 for (int d = 0; d < vdim; d++)
90 nodal_soln[vdim*n+d] += elem_soln[i]*(vis_phi[i][n](d));
91
92 return;
93} // raviart_thomas_nodal_soln
94
95
96
97unsigned int raviart_thomas_n_dofs(const ElemType t, const Order o)
98{
99 libmesh_assert_greater (o, 0);
100 switch (t)
101 {
102 case TRI6:
103 case TRI7:
104 return o*(o+2);
105 case QUAD8:
106 case QUAD9:
107 return 2*o*(o+1);
108 case TET14:
109 return o*(o+1)*(o+3)/2;
110 case HEX27:
111 return 3*o*o*(o+1);
112 case INVALID_ELEM:
113 return 0;
114 default:
115 libmesh_error_msg("ERROR: Invalid ElemType " << Utility::enum_to_string(t) << " selected for RAVIART_THOMAS FE family!");
116 }
117}
118
119
120
121unsigned int raviart_thomas_n_dofs(const Elem * e, const Order o)
122{
123 libmesh_assert(e);
124 return raviart_thomas_n_dofs(e->type(), o);
125}
126
127
128
129unsigned int raviart_thomas_n_dofs_at_node(const ElemType t,
130 const Order o,
131 const unsigned int n)
132{
133 libmesh_assert_greater (o, 0);
134 switch (t)
135 {
136 case TRI6:
137 case TRI7:
138 {
139 switch (n)
140 {
141 case 0:
142 case 1:
143 case 2:
144 return 0;
145 case 3:
146 case 4:
147 case 5:
148 return o;
149 case 6:
150 libmesh_assert_equal_to(t, TRI7);
151 return 0;
152 default:
153 libmesh_error_msg("ERROR: Invalid node ID " << n);
154 }
155 }
156 case QUAD8:
157 case QUAD9:
158 {
159 switch (n)
160 {
161 case 0:
162 case 1:
163 case 2:
164 case 3:
165 return 0;
166 case 4:
167 case 5:
168 case 6:
169 case 7:
170 return o;
171 case 8:
172 libmesh_assert_equal_to(t, QUAD9);
173 return 0;
174 default:
175 libmesh_error_msg("ERROR: Invalid node ID " << n);
176 }
177 }
178 case TET14:
179 {
180 switch (n)
181 {
182 case 0:
183 case 1:
184 case 2:
185 case 3:
186 case 4:
187 case 5:
188 case 6:
189 case 7:
190 case 8:
191 case 9:
192 return 0;
193 case 10:
194 case 11:
195 case 12:
196 case 13:
197 return o*(o+1)/2;
198 default:
199 libmesh_error_msg("ERROR: Invalid node ID " << n);
200 }
201 }
202 case HEX27:
203 {
204 switch (n)
205 {
206 case 0:
207 case 1:
208 case 2:
209 case 3:
210 case 4:
211 case 5:
212 case 6:
213 case 7:
214 case 8:
215 case 9:
216 case 10:
217 case 11:
218 case 12:
219 case 13:
220 case 14:
221 case 15:
222 case 16:
223 case 17:
224 case 18:
225 case 19:
226 return 0;
227 case 20:
228 case 21:
229 case 22:
230 case 23:
231 case 24:
232 case 25:
233 return o*o;
234 case 26:
235 return 0;
236 default:
237 libmesh_error_msg("ERROR: Invalid node ID " << n);
238 }
239 }
240 case INVALID_ELEM:
241 return 0;
242 default:
243 libmesh_error_msg("ERROR: Invalid ElemType " << Utility::enum_to_string(t) << " selected for RAVIART_THOMAS FE family!");
244 }
245}
246
247
248
249unsigned int raviart_thomas_n_dofs_at_node(const Elem & e,
250 const Order o,
251 const unsigned int n)
252{
253 return raviart_thomas_n_dofs_at_node(e.type(), o, n);
254}
255
256
257
258unsigned int raviart_thomas_n_dofs_per_elem(const ElemType t,
259 const Order o)
260{
261 libmesh_assert_greater (o, 0);
262 switch (t)
263 {
264 case TRI6:
265 case TRI7:
266 return o*(o-1);
267 case QUAD8:
268 case QUAD9:
269 return 2*o*(o-1);
270 case TET14:
271 return (o+1)*o*(o-1)/2;
272 case HEX27:
273 return 3*o*o*(o-1);
274 case INVALID_ELEM:
275 return 0;
276 default:
277 libmesh_error_msg("ERROR: Invalid ElemType " << Utility::enum_to_string(t) << " selected for RAVIART_THOMAS FE family!");
278 }
279}
280
281
282
283unsigned int raviart_thomas_n_dofs_per_elem(const Elem & e,
284 const Order o)
285{
286 return raviart_thomas_n_dofs_per_elem(e.type(), o);
287}
288
289
290#ifdef LIBMESH_ENABLE_AMR
291void raviart_thomas_compute_constraints (DofConstraints & /*constraints*/,
292 DofMap & /*dof_map*/,
293 const unsigned int /*variable_number*/,
294 const Elem * libmesh_dbg_var(elem),
295 const unsigned Dim)
296{
297 // Only constrain elements in 2,3D.
298 if (Dim == 1)
299 return;
300
301 libmesh_assert(elem);
302
303 libmesh_not_implemented();
304} // raviart_thomas_compute_constraints()
305#endif // #ifdef LIBMESH_ENABLE_AMR
306
307} // anonymous namespace
308
309#define RAVIART_LOW_D_ERROR_MESSAGE \
310 libmesh_error_msg("ERROR: This method makes no sense for low-D elements!");
311
312
313// Do full-specialization for every dimension, instead
314// of explicit instantiation at the end of this file.
315template <>
316void FE<0,RAVIART_THOMAS>::nodal_soln(const Elem *,
317 const Order,
318 const std::vector<Number> &,
319 std::vector<Number> &,
320 bool,
321 const unsigned)
322{ RAVIART_LOW_D_ERROR_MESSAGE }
323
324template <>
325void FE<1,RAVIART_THOMAS>::nodal_soln(const Elem *,
326 const Order,
327 const std::vector<Number> &,
328 std::vector<Number> &,
329 bool,
330 const unsigned)
331{ RAVIART_LOW_D_ERROR_MESSAGE }
332
333template <>
334void FE<2,RAVIART_THOMAS>::nodal_soln(const Elem * elem,
335 const Order order,
336 const std::vector<Number> & elem_soln,
337 std::vector<Number> & nodal_soln,
338 const bool add_p_level,
339 const unsigned vdim)
340{ raviart_thomas_nodal_soln(elem, order, elem_soln, 2 /*dim*/, vdim, nodal_soln, add_p_level); }
341
342template <>
343void FE<3,RAVIART_THOMAS>::nodal_soln(const Elem * elem,
344 const Order order,
345 const std::vector<Number> & elem_soln,
346 std::vector<Number> & nodal_soln,
347 const bool add_p_level,
348 const unsigned)
349{ raviart_thomas_nodal_soln(elem, order, elem_soln, 3 /*dim*/, 3 /*vdim*/, nodal_soln, add_p_level); }
350
351template <>
352void FE<0,L2_RAVIART_THOMAS>::nodal_soln(const Elem *,
353 const Order,
354 const std::vector<Number> &,
355 std::vector<Number> &,
356 bool,
357 const unsigned)
358{ RAVIART_LOW_D_ERROR_MESSAGE }
359
360template <>
361void FE<1,L2_RAVIART_THOMAS>::nodal_soln(const Elem *,
362 const Order,
363 const std::vector<Number> &,
364 std::vector<Number> &,
365 bool,
366 const unsigned)
367{ RAVIART_LOW_D_ERROR_MESSAGE }
368
369template <>
370void FE<2,L2_RAVIART_THOMAS>::nodal_soln(const Elem * elem,
371 const Order order,
372 const std::vector<Number> & elem_soln,
373 std::vector<Number> & nodal_soln,
374 const bool add_p_level,
375 const unsigned vdim)
376{ raviart_thomas_nodal_soln(elem, order, elem_soln, 2 /*dim*/, vdim, nodal_soln, add_p_level); }
377
378template <>
379void FE<3,L2_RAVIART_THOMAS>::nodal_soln(const Elem * elem,
380 const Order order,
381 const std::vector<Number> & elem_soln,
382 std::vector<Number> & nodal_soln,
383 const bool add_p_level,
384 const unsigned)
385{ raviart_thomas_nodal_soln(elem, order, elem_soln, 3 /*dim*/, 3 /*vdim*/, nodal_soln, add_p_level); }
386
387LIBMESH_FE_SIDE_NODAL_SOLN(RAVIART_THOMAS)
388LIBMESH_FE_SIDE_NODAL_SOLN(L2_RAVIART_THOMAS)
389
390
391// Do full-specialization for every dimension, instead
392// of explicit instantiation at the end of this function.
393// This could be macro-ified.
394template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
395template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
396template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
397template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
398
399template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs(const Elem *, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
400template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs(const Elem *, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
401template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs(const Elem * e, const Order o) { return raviart_thomas_n_dofs(e, o); }
402template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs(const Elem * e, const Order o) { return raviart_thomas_n_dofs(e, o); }
403
404template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
405template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
406template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
407template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
408
409template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs(const Elem *, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
410template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs(const Elem *, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
411template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs(const Elem * e, const Order o) { return raviart_thomas_n_dofs(e, o); }
412template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs(const Elem * e, const Order o) { return raviart_thomas_n_dofs(e, o); }
413
414template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
415template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
416template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(t, o, n); }
417template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(t, o, n); }
418
419template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
420template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
421template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_at_node(const Elem & e, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(e, o, n); }
422template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_at_node(const Elem & e, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(e, o, n); }
423
424template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
425template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
426template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
427template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { return 0; }
428
429template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
430template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
431template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { return 0; }
432template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs_at_node(const Elem &, const Order, const unsigned int) { return 0; }
433
434template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
435template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
436template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType t, const Order o) { return raviart_thomas_n_dofs_per_elem(t, o); }
437template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType t, const Order o) { return raviart_thomas_n_dofs_per_elem(t, o); }
438
439template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_per_elem(const Elem &, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
440template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_per_elem(const Elem &, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
441template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_per_elem(const Elem & e, const Order o) { return raviart_thomas_n_dofs_per_elem(e, o); }
442template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_per_elem(const Elem & e, const Order o) { return raviart_thomas_n_dofs_per_elem(e, o); }
443
444// L2 Raviart-Thomas elements have all their dofs per element
445template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
446template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
447template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs_per_elem(const ElemType t, const Order o) { return n_dofs(t, o); }
448template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs_per_elem(const ElemType t, const Order o) { return n_dofs(t, o); }
449
450template <> unsigned int FE<0,L2_RAVIART_THOMAS>::n_dofs_per_elem(const Elem &, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
451template <> unsigned int FE<1,L2_RAVIART_THOMAS>::n_dofs_per_elem(const Elem &, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
452template <> unsigned int FE<2,L2_RAVIART_THOMAS>::n_dofs_per_elem(const Elem & e, const Order o) { return n_dofs(&e, o); }
453template <> unsigned int FE<3,L2_RAVIART_THOMAS>::n_dofs_per_elem(const Elem & e, const Order o) { return n_dofs(&e, o); }
454
455// Raviart-Thomas FEMs are always normally continuous
456template <> FEContinuity FE<0,RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
457template <> FEContinuity FE<1,RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
458template <> FEContinuity FE<2,RAVIART_THOMAS>::get_continuity() const { return H_DIV; }
459template <> FEContinuity FE<3,RAVIART_THOMAS>::get_continuity() const { return H_DIV; }
460
461// L2 Raviart-Thomas FEMs are discontinuous
462template <> FEContinuity FE<0,L2_RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
463template <> FEContinuity FE<1,L2_RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
464template <> FEContinuity FE<2,L2_RAVIART_THOMAS>::get_continuity() const { return DISCONTINUOUS; }
465template <> FEContinuity FE<3,L2_RAVIART_THOMAS>::get_continuity() const { return DISCONTINUOUS; }
466
467// Raviart-Thomas FEMs are not hierarchic
468template <> bool FE<0,RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
469template <> bool FE<1,RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
470template <> bool FE<2,RAVIART_THOMAS>::is_hierarchic() const { return false; }
471template <> bool FE<3,RAVIART_THOMAS>::is_hierarchic() const { return false; }
472template <> bool FE<0,L2_RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
473template <> bool FE<1,L2_RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
474template <> bool FE<2,L2_RAVIART_THOMAS>::is_hierarchic() const { return false; }
475template <> bool FE<3,L2_RAVIART_THOMAS>::is_hierarchic() const { return false; }
476
477// Raviart-Thomas FEM shapes always need to be reinit'ed (because of orientation dependence)
478template <> bool FE<0,RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
479template <> bool FE<1,RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
480template <> bool FE<2,RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
481template <> bool FE<3,RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
482
483// Do L2 Raviart-Thomas FEM shapes always need to be reinit'ed because of orientation dependence?
484template <> bool FE<0,L2_RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
485template <> bool FE<1,L2_RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
486template <> bool FE<2,L2_RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
487template <> bool FE<3,L2_RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
488
489#ifdef LIBMESH_ENABLE_AMR
490template <>
491void FE<0,RAVIART_THOMAS>::compute_constraints (DofConstraints &,
492 DofMap &,
493 const unsigned int,
494 const Elem *)
495{ RAVIART_LOW_D_ERROR_MESSAGE }
496
497template <>
498void FE<1,RAVIART_THOMAS>::compute_constraints (DofConstraints &,
499 DofMap &,
500 const unsigned int,
501 const Elem *)
502{ RAVIART_LOW_D_ERROR_MESSAGE }
503
504template <>
505void FE<2,RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
506 DofMap & dof_map,
507 const unsigned int variable_number,
508 const Elem * elem)
509{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }
510
511template <>
512void FE<3,RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
513 DofMap & dof_map,
514 const unsigned int variable_number,
515 const Elem * elem)
516{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }
517
518template <>
519void FE<0,L2_RAVIART_THOMAS>::compute_constraints (DofConstraints &,
520 DofMap &,
521 const unsigned int,
522 const Elem *)
523{ RAVIART_LOW_D_ERROR_MESSAGE }
524
525template <>
526void FE<1,L2_RAVIART_THOMAS>::compute_constraints (DofConstraints &,
527 DofMap &,
528 const unsigned int,
529 const Elem *)
530{ RAVIART_LOW_D_ERROR_MESSAGE }
531
532template <>
533void FE<2,L2_RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
534 DofMap & dof_map,
535 const unsigned int variable_number,
536 const Elem * elem)
537{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }
538
539template <>
540void FE<3,L2_RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
541 DofMap & dof_map,
542 const unsigned int variable_number,
543 const Elem * elem)
544{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }
545#endif // LIBMESH_ENABLE_AMR
546
547// Specialize useless shape function methods
548template <>
549RealGradient FE<0,RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
550{ RAVIART_LOW_D_ERROR_MESSAGE }
551template <>
552RealGradient FE<0,RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
553{ RAVIART_LOW_D_ERROR_MESSAGE }
554template <>
555RealGradient FE<0,L2_RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
556{ RAVIART_LOW_D_ERROR_MESSAGE }
557template <>
558RealGradient FE<0,L2_RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
559{ RAVIART_LOW_D_ERROR_MESSAGE }
560template <>
561RealGradient FE<0,RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
562 const unsigned int,const Point &)
563{ RAVIART_LOW_D_ERROR_MESSAGE }
564template <>
565RealGradient FE<0,RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
566 const unsigned int,const Point &,const bool)
567{ RAVIART_LOW_D_ERROR_MESSAGE }
568template <>
569RealGradient FE<0,L2_RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
570 const unsigned int,const Point &)
571{ RAVIART_LOW_D_ERROR_MESSAGE }
572template <>
573RealGradient FE<0,L2_RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
574 const unsigned int,const Point &,const bool)
575{ RAVIART_LOW_D_ERROR_MESSAGE }
576
577#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
578template <>
579RealGradient FE<0,RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
580 const unsigned int,const Point &)
581{ RAVIART_LOW_D_ERROR_MESSAGE }
582template <>
583RealGradient FE<0,RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
584 const unsigned int,const Point &,const bool)
585{ RAVIART_LOW_D_ERROR_MESSAGE }
586template <>
587RealGradient FE<0,L2_RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
588 const unsigned int,const Point &)
589{ RAVIART_LOW_D_ERROR_MESSAGE }
590template <>
591RealGradient FE<0,L2_RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
592 const unsigned int,const Point &,const bool)
593{ RAVIART_LOW_D_ERROR_MESSAGE }
594
595#endif
596
597template <>
598RealGradient FE<1,RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
599{ RAVIART_LOW_D_ERROR_MESSAGE }
600template <>
601RealGradient FE<1,RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
602{ RAVIART_LOW_D_ERROR_MESSAGE }
603template <>
604RealGradient FE<1,L2_RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
605{ RAVIART_LOW_D_ERROR_MESSAGE }
606template <>
607RealGradient FE<1,L2_RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
608{ RAVIART_LOW_D_ERROR_MESSAGE }
609template <>
610RealGradient FE<1,RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
611 const unsigned int,const Point &)
612{ RAVIART_LOW_D_ERROR_MESSAGE }
613template <>
614RealGradient FE<1,RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
615 const unsigned int,const Point &,const bool)
616{ RAVIART_LOW_D_ERROR_MESSAGE }
617template <>
618RealGradient FE<1,L2_RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
619 const unsigned int,const Point &)
620{ RAVIART_LOW_D_ERROR_MESSAGE }
621template <>
622RealGradient FE<1,L2_RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
623 const unsigned int,const Point &,const bool)
624{ RAVIART_LOW_D_ERROR_MESSAGE }
625
626#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
627template <>
628RealGradient FE<1,RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
629 const unsigned int,const Point &)
630{ RAVIART_LOW_D_ERROR_MESSAGE }
631template <>
632RealGradient FE<1,RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
633 const unsigned int,const Point &,const bool)
634{ RAVIART_LOW_D_ERROR_MESSAGE }
635template <>
636RealGradient FE<1,L2_RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
637 const unsigned int,const Point &)
638{ RAVIART_LOW_D_ERROR_MESSAGE }
639template <>
640RealGradient FE<1,L2_RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
641 const unsigned int,const Point &,const bool)
642{ RAVIART_LOW_D_ERROR_MESSAGE }
643
644#endif
645
646} // namespace libMesh
dim
unsigned int dim
Definition adaptivity_ex3.C:114
libMesh::DofConstraints
The constraint matrix storage format.
Definition dof_map.h:112
libMesh::DofMap
This class handles the numbering of degrees of freedom on a mesh.
Definition dof_map.h:181
libMesh::Elem
This is the base class from which all geometric element types are derived.
Definition elem.h:96
libMesh::Elem::n_nodes
virtual unsigned int n_nodes() const =0
libMesh::Elem::type
virtual ElemType type() const =0
libMesh::Elem::p_level
unsigned int p_level() const
Definition elem.h:3125
libMesh::FEAbstract::get_refspace_nodes
static void get_refspace_nodes(const ElemType t, std::vector< Point > &nodes)
Definition fe_abstract.C:400
libMesh::FEGenericBase::build
static std::unique_ptr< FEGenericBase > build(const unsigned int dim, const FEType &type)
Builds a specific finite element type.
libMesh::FEInterface::n_shape_functions
static unsigned int n_shape_functions(const unsigned int dim, const FEType &fe_t, const ElemType t)
Definition fe_interface.C:272
libMesh::FEType
class FEType hides (possibly multiple) FEFamily and approximation orders, thereby enabling specialize...
Definition fe_type.h:197
libMesh::FE::shape
static OutputShape shape(const ElemType t, const Order o, const unsigned int i, const Point &p)
libMesh::FE::is_hierarchic
virtual bool is_hierarchic() const override
libMesh::FE::nodal_soln
static void nodal_soln(const Elem *elem, const Order o, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, bool add_p_level=true, const unsigned vdim=1)
Build the nodal soln from the element soln.
libMesh::FE::n_dofs_per_elem
static unsigned int n_dofs_per_elem(const ElemType t, const Order o)
libMesh::FE::get_continuity
virtual FEContinuity get_continuity() const override
libMesh::FE::compute_constraints
static void compute_constraints(DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to var...
libMesh::FE::n_dofs
static unsigned int n_dofs(const ElemType t, const Order o)
libMesh::FE::n_dofs_at_node
static unsigned int n_dofs_at_node(const ElemType t, const Order o, const unsigned int n)
libMesh::FE::shape_second_deriv
static OutputShape shape_second_deriv(const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
libMesh::FE::shape_deriv
static OutputShape shape_deriv(const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
libMesh::FE::shapes_need_reinit
virtual bool shapes_need_reinit() const override
libMesh::Point
A Point defines a location in LIBMESH_DIM dimensional Real space.
Definition point.h:40
libMesh::Utility::enum_to_string
std::string enum_to_string(const T e)
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::LIBMESH_DEFAULT_VECTORIZED_FE
LIBMESH_DEFAULT_VECTORIZED_FE(template<>Real FE< 0, BERNSTEIN)
Definition fe_bernstein_shape_0D.C:30
libMesh::ElemType
ElemType
Defines an enum for geometric element types.
Definition enum_elem_type.h:33
libMesh::libmesh_assert
libmesh_assert(ctx)
libMesh::L2_RAVIART_THOMAS
@ L2_RAVIART_THOMAS
Definition enum_fe_family.h:64
libMesh::LIBMESH_FE_SIDE_NODAL_SOLN
LIBMESH_FE_SIDE_NODAL_SOLN(HIERARCHIC_VEC)
Definition fe_hierarchic_vec.C:117
n_nodes
const dof_id_type n_nodes
Definition tecplot_io.C:67
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