We consider the Crouzeix–Raviart nonconforming finite element method for the Laplace equation. We present four equilibrated flux reconstructions, by direct prescription or by mixed approximation of local Neumann problems, either relying on the original simplicial mesh only or employing a dual mesh. We show that all these reconstructions coincide provided the underlying system of linear algebraic equations is solved exactly. We finally consider an inexact algebraic solve, adjust the flux reconstructions, and point out the differences.
Nous étudions la méthode des éléments finis non conformes de Crouzeix et Raviart pour lʼéquation de Laplace. Nous introduisons quatre reconstructions équilibrées du flux, par prescription directe ou par une approximation mixte de problèmes locaux de Neumann, soit sur le maillage simplectique de départ, soit sur un maillage dual. Nous montrons que toutes ces reconstructions coïncident si le système dʼéquations linéaires associé est résolu exactement. Nous considérons enfin une solution algébrique inexacte, ajustons les reconstructions du flux et indiquons les différences entre les reconstructions.
Accepted:
Published online:
Alexandre Ern 1; Martin Vohralík 2
@article{CRMATH_2013__351_1-2_77_0, author = {Alexandre Ern and Martin Vohral{\'\i}k}, title = {Four closely related equilibrated flux reconstructions for nonconforming finite elements}, journal = {Comptes Rendus. Math\'ematique}, pages = {77--80}, publisher = {Elsevier}, volume = {351}, number = {1-2}, year = {2013}, doi = {10.1016/j.crma.2013.01.001}, language = {en}, }
TY - JOUR AU - Alexandre Ern AU - Martin Vohralík TI - Four closely related equilibrated flux reconstructions for nonconforming finite elements JO - Comptes Rendus. Mathématique PY - 2013 SP - 77 EP - 80 VL - 351 IS - 1-2 PB - Elsevier DO - 10.1016/j.crma.2013.01.001 LA - en ID - CRMATH_2013__351_1-2_77_0 ER -
Alexandre Ern; Martin Vohralík. Four closely related equilibrated flux reconstructions for nonconforming finite elements. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 77-80. doi : 10.1016/j.crma.2013.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.001/
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Cited by Sources:
☆ This work was partly supported by the Groupement MoMaS (PACEN/CNRS, ANDRA, BRGM, CEA, EdF, IRSN) and by the ERT project “Enhanced oil recovery and geological sequestration of CO2: mesh adaptivity, a posteriori error control, and other advanced techniques” (LJLL UPMC/IFPEN).
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