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

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
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