Karakashian, Ohannes A.; Pascal, Frederic Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems. (English) Zbl 1140.65083 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) Cited in 35 Documents 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 PDF BibTeX XML Cite \textit{O. A. Karakashian} and \textit{F. Pascal}, SIAM J. Numer. Anal. 45, No. 2, 641--665 (2007; Zbl 1140.65083) Full Text: DOI