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Discontinuous Galerkin approximations for elliptic problems. (English) Zbl 0957.65099
A discontinuous finite element method for the approximation of elliptic problems is analyzed. The authors consider as a model problem the Laplace operator in a two-dimensional convex polygonal domain. The original formulation of this method is rewrited in a new and more elegant way, better suited for a mathematical investigation. Stability and error estimates in various norms are proven. A different stabilization based on a penalty approach is introduced and investigated.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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