The patch test for mixed formulations. (English) Zbl 0614.65115

A simple extension of patch test concepts to mixed elements is shown to provide a necessary and sufficient test for convergence. Many results of stability failure available previously from rather complex mathematics came out clearly in a conceptual patch test as failing to satisfy a necessary and simple condition. The general algebraic conditions of Babuska and Brezzi are given a simple form and an application of the patch tests serves to point out the instability of several well known formulations for incompressible problems.
Reviewer: N.F.F.Ebecken


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
35J25 Boundary value problems for second-order elliptic equations
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