Browsing by Author "Schotzau, Dominik"
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Item An a priori error analysis of the local discontinuous Galerkin method for elliptic problems(2000-04) Castillo, Paul; Cockburn, Bernardo; Perugia, Ilaria; Schotzau, DominikItem The coupling of local discontinuous Galerkin and conforming finite element methods(2000-10) Perugia, Ilaria; Schotzau, DominikItem Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems(2004-08) Houston, Paul; Schotzau, Dominik; Wihler, Thomas P.Item An HP a-priori error analysis of the DG time-stepping method for initial value problems(1999-12) Schotzau, Dominik; Schwab, ChristophItem An hp-analysis of the local discontinuous Galerkin method for diffusion problems(2001-06) Perugia, Ilaria; Schotzau, DominikWe present an $hp$-analysis of the local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes and two- and three-dimensional domains. Our estimates are optimal in the meshsize $h$ and slightly suboptimal in the polynomial approximation order $p$.Item The hp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell's equations(2001-06) Perugia, Ilaria; Schotzau, DominikThe local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in low-frequency regime is introduced and analyzed. We consider topologically non-trivial domains and heterogeneous media, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, based on a mixed formulation of the problem and on the introduction of the so-called numerical fluxes. An hp-analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained.Item Local discontinuous Galerkin methods for the Stokes system(2000-10) Cockburn, Bernardo; Kanschat, Guido; Schotzau, Dominik; Schwab, ChristophItem Optimal a priori error estimates for the version of the local discontinuous Galerkin method for convection diffusion problems(1999-02) Castillo, Paul; Cockburn, Bernardo; Schotzau, Dominik; Schwab, ChristophItem Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids(2000-04) Cockburn, Bernardo; Kanschat, Guido; Perugia, Ilaria; Schotzau, Dominik