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fe_raviart_shape_2D.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// Local includes
20#include "libmesh/fe.h"
21#include "libmesh/elem.h"
22#include "libmesh/enum_to_string.h"
23
24namespace libMesh
25{
26
27// The 2d Raviart-Thomas shape functions are just the 2d Nedelec (first kind)
28// shape functions after a 90-degree counterclockwise rotation.
29template <>
30RealGradient FE<2,RAVIART_THOMAS>::shape(const Elem * elem,
31 const Order order,
32 const unsigned int i,
33 const Point & p,
34 const bool add_p_level)
35{
36 RealGradient ND1 = FE<2,NEDELEC_ONE>::shape(elem, order, i, p, add_p_level);
37 return RealGradient(-ND1(1), ND1(0));
38}
39
40template <>
41RealGradient FE<2,L2_RAVIART_THOMAS>::shape(const Elem * elem,
42 const Order order,
43 const unsigned int i,
44 const Point & p,
45 const bool add_p_level)
46{
47 return FE<2,RAVIART_THOMAS>::shape(elem, order, i, p, add_p_level);
48}
49
50template <>
51RealGradient FE<2,RAVIART_THOMAS>::shape(const ElemType,
52 const Order,
53 const unsigned int,
54 const Point &)
55{
56 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
57 return RealGradient();
58}
59
60template <>
61RealGradient FE<2,L2_RAVIART_THOMAS>::shape(const ElemType,
62 const Order,
63 const unsigned int,
64 const Point &)
65{
66 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
67 return RealGradient();
68}
69
70template <>
71RealGradient FE<2,RAVIART_THOMAS>::shape(const FEType fet,
72 const Elem * elem,
73 const unsigned int i,
74 const Point & p,
75 const bool add_p_level)
76{
77 return FE<2,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
78}
79
80template <>
81RealGradient FE<2,L2_RAVIART_THOMAS>::shape(const FEType fet,
82 const Elem * elem,
83 const unsigned int i,
84 const Point & p,
85 const bool add_p_level)
86{
87 return FE<2,L2_RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
88}
89
90template <>
91RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const Elem * elem,
92 const Order order,
93 const unsigned int i,
94 const unsigned int j,
95 const Point & p,
96 const bool add_p_level)
97{
98 RealGradient ND1 = FE<2,NEDELEC_ONE>::shape_deriv(elem, order, i, j, p, add_p_level);
99 return RealGradient(-ND1(1), ND1(0));
100}
101
102template <>
103RealGradient FE<2,L2_RAVIART_THOMAS>::shape_deriv(const Elem * elem,
104 const Order order,
105 const unsigned int i,
106 const unsigned int j,
107 const Point & p,
108 const bool add_p_level)
109{
110 return FE<2,RAVIART_THOMAS>::shape_deriv(elem, order, i, j, p, add_p_level);
111}
112
113template <>
114RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const ElemType,
115 const Order,
116 const unsigned int,
117 const unsigned int,
118 const Point &)
119{
120 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
121 return RealGradient();
122}
123
124template <>
125RealGradient FE<2,L2_RAVIART_THOMAS>::shape_deriv(const ElemType,
126 const Order,
127 const unsigned int,
128 const unsigned int,
129 const Point &)
130{
131 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
132 return RealGradient();
133}
134
135template <>
136RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const FEType fet,
137 const Elem * elem,
138 const unsigned int i,
139 const unsigned int j,
140 const Point & p,
141 const bool add_p_level)
142{
143 return FE<2,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
144}
145
146template <>
147RealGradient FE<2,L2_RAVIART_THOMAS>::shape_deriv(const FEType fet,
148 const Elem * elem,
149 const unsigned int i,
150 const unsigned int j,
151 const Point & p,
152 const bool add_p_level)
153{
154 return FE<2,L2_RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
155}
156
157#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
158
159template <>
160RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
161 const Order order,
162 const unsigned int i,
163 const unsigned int j,
164 const Point & p,
165 const bool add_p_level)
166{
167 RealGradient ND1 = FE<2,NEDELEC_ONE>::shape_second_deriv(elem, order, i, j, p, add_p_level);
168 return RealGradient(-ND1(1), ND1(0));
169}
170
171template <>
172RealGradient FE<2,L2_RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
173 const Order order,
174 const unsigned int i,
175 const unsigned int j,
176 const Point & p,
177 const bool add_p_level)
178{
179 return FE<2,RAVIART_THOMAS>::shape_second_deriv(elem, order, i, j, p, add_p_level);
180}
181
182template <>
183RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const ElemType,
184 const Order,
185 const unsigned int,
186 const unsigned int,
187 const Point &)
188{
189 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
190 return RealGradient();
191}
192
193template <>
194RealGradient FE<2,L2_RAVIART_THOMAS>::shape_second_deriv(const ElemType,
195 const Order,
196 const unsigned int,
197 const unsigned int,
198 const Point &)
199{
200 libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
201 return RealGradient();
202}
203
204template <>
205RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
206 const Elem * elem,
207 const unsigned int i,
208 const unsigned int j,
209 const Point & p,
210 const bool add_p_level)
211{
212 return FE<2,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
213}
214
215template <>
216RealGradient FE<2,L2_RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
217 const Elem * elem,
218 const unsigned int i,
219 const unsigned int j,
220 const Point & p,
221 const bool add_p_level)
222{
223 return FE<2,L2_RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
224}
225
226#endif
227
228} // namespace libMesh
libMesh::Elem
This is the base class from which all geometric element types are derived.
Definition elem.h:96
libMesh::FEType
class FEType hides (possibly multiple) FEFamily and approximation orders, thereby enabling specialize...
Definition fe_type.h:197
libMesh::FEType::order
OrderWrapper order
The approximation order of the element (at 0 p-refinement level).
Definition fe_type.h:203
libMesh::FE::shape
static OutputShape shape(const ElemType t, const Order o, const unsigned int i, const Point &p)
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::Point
A Point defines a location in LIBMESH_DIM dimensional Real space.
Definition point.h:40
libMesh
The libMesh namespace provides an interface to certain functionality in the library.
libMesh::ElemType
ElemType
Defines an enum for geometric element types.
Definition enum_elem_type.h:33
libMesh::RealGradient
RealVectorValue RealGradient
Definition hp_coarsentest.h:49
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