\(L^ p\)-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems. (English) Zbl 0831.65110

Babuska, Ivo (ed.) et al., Modeling, mesh generation, and adaptive numerical methods for partial differential equations. Based on the proceedings of the 1993 IMA summer program held at IMA, University of Minnesota, Minneapolis, MN, USA. New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 75, 187-199 (1995).
Summary: We consider mixed finite element methods for the approximation of linear and quasilinear second-order elliptic problems. A class of postprocessing methods for improving mixed finite element solutions is analyzed. In particular, error estimates in \(L^p\), \(1 \leq p \leq \infty\), are given. These postprocessing methods are applicable to all the existing mixed methods, and can easily be implemented. Furthermore, they are local and thus fully parallelizable.
For the entire collection see [Zbl 0822.00013].


65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations