Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition∗
Institut für Numerische Simulation, Universität Bonn, Wegelerstraße 6, 53115 Bonn, Germany.
Received: 21 September 2015
Revised: 23 March 2016
Accepted: 5 April 2016
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.
Mathematics Subject Classification: 65N30 / 76M10 / 65N12
Key words: Linear elasticity / Stokes equations / non-conforming FEM / Helmholtz decomposition / mixed FEM / adaptive FEM / optimality
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