Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems. (English) Zbl 1140.65083

Karakashian, Ohannes A.; Pascal, Frederic

SIAM J. Numer. Anal. 45, No. 2, 641-665 (2007).

The authors develop a complete mathematical theory and analysis for adaptive discontinuous Galerkin approximations of second-order elliptic equations. A number of theorems and lemmas is presented for validation and existence of the theory. Finally numerical experiments are presented for verification and validation of the proposed theory. Interesting work.

Reviewer: Prabhat Kumar Mahanti (Saint John)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65N15	Error bounds for boundary value problems involving PDEs

Keywords:

convergence; a posteriori estimates; adaptive discontinuous Galerkin approximations; second-order elliptic equations; numerical experiments