## Asymptotic expansions and $$L^{\infty}$$-error estimates for mixed finite element methods for second order elliptic problems.(English)Zbl 0676.65109

A mixed formation of a second order elliptic problem is considered and asymptotic properties of mixed finite element approximations which are obtained by using new families of finite element spaces (BDM spaces) [cf. F. Brezzi, J. Douglas jun. and L. D. Marini, ibid. 47, 217-235 (1985; Zbl 0599.65072)] are studied. Assuming the only geometric requirement of quasi-uniform regularity on the triangulation of the domain, asymptotic expansions for the first order approximation of the scalar field are desired. It is shown that Richardson extrapolation can be applied to increase the accuracy of the approximations. Another application of the asymptotic expansion which is called error corrected method is also considered.
Reviewer: H.P.Dikshit

### MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations

Zbl 0599.65072
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### References:

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