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Analysis of the DPG method for the Poisson equation. (English) Zbl 1237.65122

The authors present an analysis of a discontinuous Petrov Galerkin (DPG) method for the Poisson equation. The purpose of the present contribution is to provide new techniques in order to analyse DPG in higher space dimensions. The authors first recall with a salient abstract for the DPG method and then they develop bilinear and linear forms that constitute the PDG method. An analysis for the error of the method is presented and how the analysis provided in the present paper can be extended to more general second order elliptic equation is sketched.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N15 Error bounds for boundary value problems involving PDEs
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