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A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. (English) Zbl 1010.65045
The authors discuss some discontinuous Galerkin approximations for solving elliptic problems. In these approximations the basic bilinear form is asymmetric. Three forms are discussed as follows:
(1) non-symmetric interior penalty Galerkin where there is a penalty term on edges;
(2) non-symmetric constrained Galerkin where there is one constraint per edge;
(3) discontinuous Galerkin which involves a total lack of constraint.
Error estimates are obtained involving the mesh size and the degree of polynormal approximation. The tone of the paper is highly abstract involving a number of spaces. The analysis is illustrated by an example showing how the error depends on the number of degrees of freedom in the analysis.

MSC:
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
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