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**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

### MSC:

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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\textit{O. C. Zienkiewicz} et al., Int. J. Numer. Methods Eng. 23, 1873--1883 (1986; Zbl 0614.65115)

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### References:

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