Unified analysis of discontinuous Galerkin methods for elliptic problems. (English) Zbl 1008.65080

Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella

SIAM J. Numer. Anal. 39, No. 5, 1749-1779 (2002).

Summary: We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.

MSC:

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

Keywords:

second-order elliptic problems; discontinuous Galerkin methods; interior penalty; comparison of methods; Poisson equation; finite element method; error bounds; stability