This paper introduces new mixed finite element methods (FEMs) of degree 1 for the equations of linear elasticity and the Stokes equations based on Helmholtz decompositions. These FEMs are robust with respect to the incompressible limit and also allow for mixed boundary conditions. Adaptive algorithms driven by efficient and reliable residual-based error estimators are introduced and proved to converge with optimal rate in the case of the Stokes equations with pure Dirichlet boundary.
Accepté le :
DOI : 10.1051/m2an/2016024
Mots-clés : Linear elasticity, Stokes equations, non-conforming FEM, Helmholtz decomposition, mixed FEM, adaptive FEM, optimality
@article{M2AN_2017__51_2_399_0, author = {Schedensack, Mira}, title = {Mixed finite element methods for linear elasticity and the {Stokes} equations based on the {Helmholtz} decomposition}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {399--425}, publisher = {EDP-Sciences}, volume = {51}, number = {2}, year = {2017}, doi = {10.1051/m2an/2016024}, mrnumber = {3626404}, zbl = {1398.76125}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2016024/} }
TY - JOUR AU - Schedensack, Mira TI - Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 399 EP - 425 VL - 51 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016024/ DO - 10.1051/m2an/2016024 LA - en ID - M2AN_2017__51_2_399_0 ER -
%0 Journal Article %A Schedensack, Mira %T Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 399-425 %V 51 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016024/ %R 10.1051/m2an/2016024 %G en %F M2AN_2017__51_2_399_0
Schedensack, Mira. Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 399-425. doi : 10.1051/m2an/2016024. http://archive.numdam.org/articles/10.1051/m2an/2016024/
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