Geodesic
Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition
Schedensack, Mira1
1 Institut für Numerische Simulation, Universität Bonn, Wegelerstraße 6, 53115 Bonn, Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 399-425

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016024
Classification : 65N30, 76M10, 65N12
Keywords: Linear elasticity, Stokes equations, non-conforming FEM, Helmholtz decomposition, mixed FEM, adaptive FEM, optimality

Schedensack, Mira 1

1 Institut für Numerische Simulation, Universität Bonn, Wegelerstraße 6, 53115 Bonn, Germany. 
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     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},
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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

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