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crouzeix_raviart.h
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1/*
2 * Copyright (c) 2012-2015: G-CSC, Goethe University Frankfurt
3 * Author: Christian Wehner
4 *
5 * This file is part of UG4.
6 *
7 * UG4 is free software: you can redistribute it and/or modify it under the
8 * terms of the GNU Lesser General Public License version 3 (as published by the
9 * Free Software Foundation) with the following additional attribution
10 * requirements (according to LGPL/GPL v3 §7):
11 *
12 * (1) The following notice must be displayed in the Appropriate Legal Notices
13 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
14 *
15 * (2) The following notice must be displayed at a prominent place in the
16 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
17 *
18 * (3) The following bibliography is recommended for citation and must be
19 * preserved in all covered files:
20 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
21 * parallel geometric multigrid solver on hierarchically distributed grids.
22 * Computing and visualization in science 16, 4 (2013), 151-164"
23 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
24 * flexible software system for simulating pde based models on high performance
25 * computers. Computing and visualization in science 16, 4 (2013), 165-179"
26 *
27 * This program is distributed in the hope that it will be useful,
28 * but WITHOUT ANY WARRANTY; without even the implied warranty of
29 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
30 * GNU Lesser General Public License for more details.
31 */
32
33#ifndef __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__CROUZEIX_RAVIART__
34#define __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__CROUZEIX_RAVIART__
35
36#include "lib_grid/grid/grid_base_objects.h"
37#include "lib_disc/reference_element/reference_element_util.h"
38#include "lib_disc/local_finite_element/local_shape_function_set.h"
39
40namespace ug{
41
42
44template <typename TRefElem>
45class CrouzeixRaviartBase
46{
47 public:
49 static const int dim = TRefElem::dim;
50
52 static const size_t nsh = TRefElem::numSides;
53
54 public:
56 CrouzeixRaviartBase()
57 {
58 for(size_t i = 0; i < nsh; ++i)
59 m_vLocalDoF[i] = LocalDoF(dim-1, i, 0);
60 }
61
63 ReferenceObjectID roid() const {return TRefElem::REFERENCE_OBJECT_ID;}
64
66 size_t num_dof() const {return nsh;};
67 size_t num_sh() const {return nsh;}
68
70 size_t num_dof(ReferenceObjectID type) const
71 {
72 if(ReferenceElementDimension(type) == dim-1) return 1;
73 else return 0;
74 }
75
77 const LocalDoF& local_dof(size_t dof) const {return m_vLocalDoF[dof];}
78
80 bool exact_position_available() const {return true;};
81
83 bool continuous() const {return false;}
84
85 protected:
87 LocalDoF m_vLocalDoF[nsh];
88};
89
91template <typename TRefElem>
92class CrouzeixRaviartLSFS;
93
95// ReferenceTriangle
96//
97// function space span {1,x,y}
98//
100
101template <>
102class CrouzeixRaviartLSFS<ReferenceTriangle>
103: public CrouzeixRaviartBase<ReferenceTriangle>,
104 public BaseLSFS<CrouzeixRaviartLSFS<ReferenceTriangle>, 2>
105{
106 public:
108 static const int dim = 2;
109
110 public:
112 bool position(size_t i, MathVector<dim>& pos) const
113 {
114 switch(i)
115 {
116 case 0: pos[0] = 0.5;
117 pos[1] = 0.0; return true;
118 case 1: pos[0] = 0.5;
119 pos[1] = 0.5; return true;
120 case 2: pos[0] = 0.0;
121 pos[1] = 0.5; return true;
122 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
123 " not found. Only "<<nsh<<" shapes present.");
124 }
125 }
126
128 number shape(const size_t i, const MathVector<dim>& x) const
129 {
130 switch(i)
131 {
132 case 0: return 1-2*x[1];
133 case 1: return -1+2*x[0]+2*x[1];
134 case 2: return 1-2*x[0];
135 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
136 " not found. Only "<<nsh<<" shapes present.");
137 }
138 }
139
141 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
142 {
143 switch(i)
144 {
145 case 0: g[0] = 0.0;
146 g[1] = -2.0; return;
147 case 1: g[0] = 2.0;
148 g[1] = 2.0; return;
149 case 2: g[0] = -2.0;
150 g[1] = 0.0; return;
151 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
152 " not found. Only "<<nsh<<" shapes present.");
153 }
154 }
155};
156
157
159// ReferenceQuadrilateral
160//
161// function space span {1,x,y,x^2-y^2}
162//
164
165template <>
166class CrouzeixRaviartLSFS<ReferenceQuadrilateral>
167: public CrouzeixRaviartBase<ReferenceQuadrilateral>,
168 public BaseLSFS<CrouzeixRaviartLSFS<ReferenceQuadrilateral>, 2>
169{
170 public:
172 static const int dim = 2;
173
174 public:
176 bool position(size_t i, MathVector<dim>& pos) const
177 {
178 switch(i)
179 {
180 case 0: pos[0] = 0.5;
181 pos[1] = 0.0; return true;
182 case 1: pos[0] = 1.0;
183 pos[1] = 0.5; return true;
184 case 2: pos[0] = 0.5;
185 pos[1] = 1.0; return true;
186 case 3: pos[0] = 0.0;
187 pos[1] = 0.5; return true;
188 return true;
189 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
190 " not found. Only "<<nsh<<" shapes present.");
191 }
192 }
193
195 number shape(const size_t i, const MathVector<dim>& x) const
196 {
197 switch(i)
198 {
199 case 0: return 0.75+x[0]-2*x[1]-x[0]*x[0]+x[1]*x[1];
200 case 1: return -0.25+x[1]+x[0]*x[0]-x[1]*x[1];
201 case 2: return -0.25+x[0]-x[0]*x[0]+x[1]*x[1];
202 case 3: return 0.75-2*x[0]+x[1]+x[0]*x[0]-x[1]*x[1];
203 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
204 " not found. Only "<<nsh<<" shapes present.");
205 }
206 }
207
209 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
210 {
211 switch(i)
212 {
213 case 0: g[0] = 1-2*x[0];
214 g[1] = -2.0+2*x[1]; return;
215 case 1: g[0] = 2.0*x[0];
216 g[1] = 1-2.0*x[1]; return;
217 case 2: g[0] = 1-2.0*x[0];
218 g[1] = 2*x[1]; return;
219 case 3: g[0] = -2+2*x[0];
220 g[1] = 1-2*x[1]; return;
221 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
222 " not found. Only "<<nsh<<" shapes present.");
223 }
224 }
225};
226
228// ReferenceTetrahedron
229//
230// function space span {1,x,y,z}
231//
233
234template <>
235class CrouzeixRaviartLSFS<ReferenceTetrahedron>
236: public CrouzeixRaviartBase<ReferenceTetrahedron>,
237 public BaseLSFS<CrouzeixRaviartLSFS<ReferenceTetrahedron>, 3>
238{
239 public:
241 static const int dim = ReferenceTetrahedron::dim;
242
243 public:
245 bool position(size_t i, MathVector<dim>& pos) const
246 {
247 switch(i)
248 {
249 case 0: pos[0] = 1.0/3.0;
250 pos[1] = 1.0/3.0;
251 pos[2] = 0.0; return true;
252 case 1: pos[0] = 1.0/3.0;
253 pos[1] = 1.0/3.0;
254 pos[2] = 1.0/3.0; return true;
255 case 2: pos[0] = 0.0;
256 pos[1] = 1.0/3.0;
257 pos[2] = 1.0/3.0; return true;
258 case 3: pos[0] = 1.0/3.0;
259 pos[1] = 0.0;
260 pos[2] = 1.0/3.0; return true;
261 return true;
262 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
263 " not found. Only "<<nsh<<" shapes present.");
264 }
265 }
266
268 number shape(const size_t i, const MathVector<dim>& x) const
269 {
270 switch(i)
271 {
272 case 0: return 1 - 3*x[2];;
273 case 1: return -2 + 3*x[0]+3*x[1]+3*x[2];
274 case 2: return 1 - 3*x[0];
275 case 3: return 1 - 3*x[1];
276 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
277 " not found. Only "<<nsh<<" shapes present.");
278 }
279 }
280
282 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
283 {
284 switch(i)
285 {
286 case 0: g[0] = 0.0;
287 g[1] = 0.0;
288 g[2] = -3.0;return;
289 case 1: g[0] = 3.0;
290 g[1] = 3.0;
291 g[2] = 3.0;return;
292 case 2: g[0] = -3.0;
293 g[1] = 0.0;
294 g[2] = 0.0;return;
295 case 3: g[0] = 0.0;
296 g[1] = -3;
297 g[2] = 0.0;return;
298 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
299 " not found. Only "<<nsh<<" shapes present.");
300 }
301 }
302};
303
304
306// ReferenceHexahedron
307//
308// function space span {1,x,y,z,x^2-y^2,y^2-z^2}
309//
311
312template <>
313class CrouzeixRaviartLSFS<ReferenceHexahedron>
314: public CrouzeixRaviartBase<ReferenceHexahedron>,
315 public BaseLSFS<CrouzeixRaviartLSFS<ReferenceHexahedron>, 3>
316{
317 public:
319 static const int dim = ReferenceHexahedron::dim;
320
321 public:
323 bool position(size_t i, MathVector<dim>& pos) const
324 {
325 switch(i)
326 {
327 case 0: pos[0] = 0.5;
328 pos[1] = 0.5;
329 pos[2] = 0.0;return true;
330 case 1: pos[0] = 0.5;
331 pos[1] = 0.0;
332 pos[2] = 0.5; return true;
333 case 2: pos[0] = 1.0;
334 pos[1] = 0.5;
335 pos[2] = 0.5; return true;
336 case 3: pos[0] = 0.5;
337 pos[1] = 1.0;
338 pos[2] = 0.5; return true;
339 case 4: pos[0] = 0.0;
340 pos[1] = 0.5;
341 pos[2] = 0.5; return true;
342 case 5: pos[0] = 0.5;
343 pos[1] = 0.5;
344 pos[2] = 1.0; return true;
345 return true;
346 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
347 " not found. Only "<<nsh<<" shapes present.");
348 }
349 }
350
352 number shape(const size_t i, const MathVector<dim>& x) const
353 {
354 switch(i)
355 {
356 case 0: return 1.0/3.0*(2 + 2*x[0] + 2*x[1] - 7*x[2]-2*x[0]*x[0]-2*x[1]*x[1]+4*x[2]*x[2]);
357 case 1: return 1.0/3.0*(2+2*x[0]-7*x[1]+2*x[2]-2*x[0]*x[0]+4*x[1]*x[1]-2*x[2]*x[2]);
358 case 2: return 1.0/3.0*(-1-x[0]+2*x[1]+2*x[2]+4*x[0]*x[0]-2*x[1]*x[1]-2*x[2]*x[2]);
359 case 3: return 1.0/3.0*(-1+2*x[0]-x[1]+2*x[2]-2*x[0]*x[0]+4*x[1]*x[1]-2*x[2]*x[2]);
360 case 4: return 1.0/3.0*(2-7*x[0]+2*x[1]+2*x[2]+4*x[0]*x[0]-2*x[1]*x[1]-2*x[2]*x[2]);
361 case 5: return 1.0/3.0*(-1+2*x[0]+2*x[1]-x[2]-2*x[0]*x[0]-2*x[1]*x[1]+4*x[2]*x[2]);
362 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
363 " not found. Only "<<nsh<<" shapes present.");
364 }
365 }
366
368 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
369 {
370 switch(i)
371 {
372 case 0: g[0] = 1.0/3.0*(2-4*x[0]);
373 g[1] = 1.0/3.0*(2-4*x[1]);
374 g[2] = 1.0/3.0*(-7+8*x[2]);return;
375 case 1: g[0] = 1.0/3.0*(2-4*x[0]);
376 g[1] = 1.0/3.0*(-7+8*x[1]);
377 g[2] = 1.0/3.0*(2-4*x[2]);return;
378 case 2: g[0] = 1.0/3.0*(-1+8*x[0]);
379 g[1] = 1.0/3.0*(2-4*x[1]);
380 g[2] = 1.0/3.0*(2-4*x[2]);return;
381 case 3: g[0] = 1.0/3.0*(2-4*x[0]);
382 g[1] = 1.0/3.0*(-1+8*x[1]);
383 g[2] = 1.0/3.0*(2-4*x[2]);return;
384 case 4: g[0] = 1.0/3.0*(-7+8*x[0]);
385 g[1] = 1.0/3.0*(2-4*x[1]);
386 g[2] = 1.0/3.0*(2-4*x[2]);return;
387 case 5: g[0] = 1.0/3.0*(2-4*x[0]);
388 g[1] = 1.0/3.0*(2-4*x[1]);
389 g[2] = 1.0/3.0*(-1+8*x[2]);return;
390 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
391 " not found. Only "<<nsh<<" shapes present.");
392 }
393 }
394};
395
397// ReferencePrism
398//
399// function space span {1,x,y,z,x^2-y^2-z^2}
400//
402
403template <>
404class CrouzeixRaviartLSFS<ReferencePrism>
405: public CrouzeixRaviartBase<ReferencePrism>,
406 public BaseLSFS<CrouzeixRaviartLSFS<ReferencePrism>, 3>
407{
408 public:
410 static const int dim = 3;
411
412 public:
414 bool position(size_t i, MathVector<dim>& pos) const
415 {
416 switch(i)
417 {
418 case 0: pos[0] = 1.0/3.0;
419 pos[1] = 1.0/3.0;
420 pos[2] = 0.0;return true;
421 case 1: pos[0] = 0.5;
422 pos[1] = 0.0;
423 pos[2] = 0.5; return true;
424 case 2: pos[0] = 0.5;
425 pos[1] = 0.5;
426 pos[2] = 0.5; return true;
427 case 3: pos[0] = 0.0;
428 pos[1] = 0.5;
429 pos[2] = 0.5; return true;
430 case 4: pos[0] = 1.0/3.0;
431 pos[1] = 1.0/3.0;
432 pos[2] = 1.0; return true;
433 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
434 " not found. Only "<<nsh<<" shapes present.");
435 }
436 }
437
439 number shape(const size_t i, const MathVector<dim>& x) const
440 {
441 switch(i)
442 {
443 case 0: return 1+x[0]-x[1]-3*x[2]-2*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
444 case 1: return 1.0/3.0*(2-2*x[0]-4*x[1]+4*x[2]+4*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]));
445 case 2: return 1.0/3.0*(-4+4*x[0]+8*x[1]+4*x[2]+4*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]));
446 case 3: return 1.0/3.0*(2-8*x[0]+2*x[1]+4*x[2]+4*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]));
447 case 4: return x[0]-x[1]-x[2]-2*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
448 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
449 " not found. Only "<<nsh<<" shapes present.");
450 }
451 }
452
454 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
455 {
456 switch(i)
457 {
458 case 0: g[0] = 1-4*x[0];
459 g[1] = -1+4*x[1];
460 g[2] = -3+4*x[2];return;
461 case 1: g[0] = 1.0/3.0*(-2+8*x[0]);
462 g[1] = 1.0/3.0*(-4-8*x[1]);
463 g[2] = 1.0/3.0*(4-8*x[2]);return;
464 case 2: g[0] = 1.0/3.0*(4+8*x[0]);
465 g[1] = 1.0/3.0*(8-8*x[1]);
466 g[2] = 1.0/3.0*(4-8*x[2]);return;
467 case 3: g[0] = 1.0/3.0*(-8+8*x[0]);
468 g[1] = 1.0/3.0*(2-8*x[1]);
469 g[2] = 1.0/3.0*(4-8*x[2]);return;
470 case 4: g[0] = 1-4*x[0];
471 g[1] = -1+4*x[1];
472 g[2] = -1+4*x[2];return;
473 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
474 " not found. Only "<<nsh<<" shapes present.");
475 }
476 }
477};
478
479
481// ReferencePyramid
482//
483// function space span {1,x,y,z,x^2-y^2-z^2}
484//
486
487template <>
488class CrouzeixRaviartLSFS<ReferencePyramid>
489: public CrouzeixRaviartBase<ReferencePyramid>,
490 public BaseLSFS<CrouzeixRaviartLSFS<ReferencePyramid>, 3>
491{
492 public:
494 static const int dim = 3;
495
496 public:
498 bool position(size_t i, MathVector<dim>& pos) const
499 {
500 switch(i)
501 {
502 case 0: pos[0] = 0.5;
503 pos[1] = 0.5;
504 pos[2] = 0.0;return true;
505 case 1: pos[0] = 1.0/3.0;
506 pos[1] = 0.0;
507 pos[2] = 1.0/3.0; return true;
508 case 2: pos[0] = 2.0/3.0;
509 pos[1] = 1.0/3.0;
510 pos[2] = 1.0/3.0; return true;
511 case 3: pos[0] = 1.0/3.0;
512 pos[1] = 2.0/3.0;
513 pos[2] = 1.0/3.0; return true;
514 case 4: pos[0] = 0.0;
515 pos[1] = 1.0/3.0;
516 pos[2] = 1.0/3.0; return true;
517 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
518 " not found. Only "<<nsh<<" shapes present.");
519 }
520 }
521
523 number shape(const size_t i, const MathVector<dim>& x) const
524 {
525 switch(i)
526 {
527 case 0: return 1-3*x[2];
528 case 1: return 0.75+1.5*x[0]-3*x[1]-0.75*x[2]-2.25*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
529 case 2: return -0.75+1.5*x[1]+2.25*x[2]+2.25*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
530 case 3: return -0.75+1.5*x[0]+0.75*x[2]-2.25*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
531 case 4: return 0.75-3*x[0]+1.5*x[1]+0.75*x[2]+2.25*(x[0]*x[0]-x[1]*x[1]-x[2]*x[2]);
532 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
533 " not found. Only "<<nsh<<" shapes present.");
534 }
535 }
536
538 void grad(MathVector<dim>& g, const size_t i, const MathVector<dim>& x) const
539 {
540 switch(i)
541 {
542 case 0: g[0] = 0.0;
543 g[1] = 0.0;
544 g[2] = -3.0;return;
545 case 1: g[0] = 1.5-4.5*x[0];
546 g[1] = -3+4.5*x[1];
547 g[2] = -0.75+4.5*x[2];return;
548 case 2: g[0] = 4.5*x[0];
549 g[1] = 1.5-4.5*x[1];
550 g[2] = 2.25-4.5*x[2];return;
551 case 3: g[0] = 1.5-4.5*x[0];
552 g[1] = 4.5*x[1];
553 g[2] = 0.75+4.5*x[2];return;
554 case 4: g[0] = -3+4.5*x[0];
555 g[1] = 1.5-4.5*x[1];
556 g[2] = 0.75-4.5*x[2];return;
557 default: UG_THROW("CrouzeixRaviartLSFS: shape function "<<i<<
558 " not found. Only "<<nsh<<" shapes present.");
559 }
560 }
561};
562
563
564} //namespace ug
565
566#endif /* __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__CROUZEIX_RAVIART__ */
567
ug::BaseLSFS
static interface for trial spaces
Definition local_shape_function_set.h:176
ug::CrouzeixRaviartBase
Crouzeix - Raviart Set.
Definition crouzeix_raviart.h:46
ug::CrouzeixRaviartBase::nsh
static const size_t nsh
Number of shape functions.
Definition crouzeix_raviart.h:52
ug::CrouzeixRaviartBase::exact_position_available
bool exact_position_available() const
returns if the local dof position are exact
Definition crouzeix_raviart.h:80
ug::CrouzeixRaviartBase::roid
ReferenceObjectID roid() const
returns the type of reference element
Definition crouzeix_raviart.h:63
ug::CrouzeixRaviartBase::m_vLocalDoF
LocalDoF m_vLocalDoF[nsh]
association to elements
Definition crouzeix_raviart.h:87
ug::CrouzeixRaviartBase::local_dof
const LocalDoF & local_dof(size_t dof) const
returns the dof storage
Definition crouzeix_raviart.h:77
ug::CrouzeixRaviartBase::CrouzeixRaviartBase
CrouzeixRaviartBase()
constructor
Definition crouzeix_raviart.h:56
ug::CrouzeixRaviartBase::dim
static const int dim
dimension of reference element
Definition crouzeix_raviart.h:49
ug::CrouzeixRaviartBase::continuous
bool continuous() const
returns if space constructs continuous functions
Definition crouzeix_raviart.h:83
ug::CrouzeixRaviartBase::num_dof
size_t num_dof() const
returns the total number of DoFs on the finite element
Definition crouzeix_raviart.h:66
ug::CrouzeixRaviartBase::num_dof
size_t num_dof(ReferenceObjectID type) const
returns the number of DoFs on a sub-geometric object type
Definition crouzeix_raviart.h:70
ug::CrouzeixRaviartBase::num_sh
size_t num_sh() const
Definition crouzeix_raviart.h:67
ug::CrouzeixRaviartLSFS< ReferenceHexahedron >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:352
ug::CrouzeixRaviartLSFS< ReferenceHexahedron >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:368
ug::CrouzeixRaviartLSFS< ReferenceHexahedron >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:323
ug::CrouzeixRaviartLSFS< ReferencePrism >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:454
ug::CrouzeixRaviartLSFS< ReferencePrism >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:439
ug::CrouzeixRaviartLSFS< ReferencePrism >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:414
ug::CrouzeixRaviartLSFS< ReferencePyramid >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:498
ug::CrouzeixRaviartLSFS< ReferencePyramid >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:523
ug::CrouzeixRaviartLSFS< ReferencePyramid >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:538
ug::CrouzeixRaviartLSFS< ReferenceQuadrilateral >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:209
ug::CrouzeixRaviartLSFS< ReferenceQuadrilateral >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:176
ug::CrouzeixRaviartLSFS< ReferenceQuadrilateral >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:195
ug::CrouzeixRaviartLSFS< ReferenceTetrahedron >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:282
ug::CrouzeixRaviartLSFS< ReferenceTetrahedron >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:268
ug::CrouzeixRaviartLSFS< ReferenceTetrahedron >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:245
ug::CrouzeixRaviartLSFS< ReferenceTriangle >::shape
number shape(const size_t i, const MathVector< dim > &x) const
evaluates the shape function
Definition crouzeix_raviart.h:128
ug::CrouzeixRaviartLSFS< ReferenceTriangle >::grad
void grad(MathVector< dim > &g, const size_t i, const MathVector< dim > &x) const
evaluates the gradient of the shape function
Definition crouzeix_raviart.h:141
ug::CrouzeixRaviartLSFS< ReferenceTriangle >::position
bool position(size_t i, MathVector< dim > &pos) const
local position of DoF i
Definition crouzeix_raviart.h:112
ug::CrouzeixRaviartLSFS
Lagrange Shape Function Set without virtual functions and fixed order.
Definition crouzeix_raviart.h:92
ug::LocalDoF
Definition local_dof_set.h:58
ug::MathVector
a mathematical Vector with N entries.
Definition math_vector.h:97
ug::ReferenceHexahedron
reference element for a hexahedron
Definition reference_element.h:648
ug::ReferenceHexahedron::dim
static const int dim
dimension of reference element
Definition reference_element.h:654
ug::ReferencePrism
Definition reference_element.h:595
ug::ReferencePyramid
Definition reference_element.h:546
ug::ReferenceQuadrilateral
Definition reference_element.h:445
ug::ReferenceTetrahedron
Definition reference_element.h:494
ug::ReferenceTetrahedron::dim
static const int dim
dimension of reference element
Definition reference_element.h:500
ug::ReferenceTriangle
Definition reference_element.h:394
grid_base_objects.h
UG_THROW
#define UG_THROW(msg)
Definition error.h:57
number
double number
Definition types.h:124
local_shape_function_set.h
ug
the ug namespace
ug::ReferenceObjectID
ReferenceObjectID
these ids are used to identify the shape of a geometric object.
Definition grid_base_objects.h:74
ug::ReferenceElementDimension
int ReferenceElementDimension(ReferenceObjectID roid)
returns the reference element dimension at run-time
Definition reference_element_util.h:40
reference_element_util.h