On Discontinuous Galerkin Methods for Elliptic Problems with Discontinuous Coefficients

By Maksymilian Dryja. 2003

118 citations recorded by the source corpus.

Abstract Discontinuous Galerkin methods for elliptic problems with discontinuous coefficients are discussed. First the error bound of the methods is analyzed. Then a multilevel additive Schwarz preconditioner for one of the discrete problems is designed and analyzed. Although the preconditioner is not optimal it is very well suited for parallel computations and its rate of convergence is independent of the jumps of coefficients.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ab070ee5d3013089c851d6a91e9a25d6d9e51082

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

CutFEM: Discretizing geometry and partial differential equations (2015, methodology): “This choice of weights was first considered in the context of discontinuous Galerkin methods in [36] and then for Nitsche’s method in [37].”
Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems (2016, unknown): “See for example [2], [22], [8], [11], [16], [14], [4], [9], [5], [18], [17], [23], [7], [3], [21], [1], [19], [15].”
Generalized multiscale finite element methods (GMsFEM) (2013, methodology): “Discontinuous Galerkin coupling One can also use the discontinuous Galerkin (DG) approach (see also [9, 22, 50]) to couple multiscale basis functions.”