Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. (English) Zbl 0567.65078

This paper is concerned with a technique for implementing certain mixed finite elements based on the use of Lagrange multipliers to impose interelement continuity. The matrices arising from this implementation are positive definite. Considering some well-known mixed methods, namely the Raviart-Thomas methods for second order elliptic problems and the Hellan-Herrmann-Johnson method for biharmonic problems, the authors show that the computed Lagrange multipliers may be exploited in a simple postprocess to produce better approximation of the original variables. Moreover, an equivalence between the mixed methods and certain modified versions of nonconforming methods is considered.
Reviewer: J.Lovíšek


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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