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A posteriori error estimation for discontinuous Galerkin finite element approximation. (English) Zbl 1151.65083
The author presents computable error bounds for a discrete Galerkin method for the Poisson equation on polygonal domains in the plane. The basis functions are piecewise linear functions on triangles. Results are given in two norms, one formed by summing energy norms over the cells, and the other including the jumps across interior cell edges.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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