Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition

Schedensack, Mira

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 399-425.

This paper introduces new mixed finite element methods (FEMs) of degree $\ge$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.

Classification : 65N30, 76M10, 65N12
Mots clés : Linear elasticity, Stokes equations, non-conforming FEM, Helmholtz decomposition, mixed FEM, adaptive FEM, optimality

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