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Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data

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Georgoulis, E. H. and Pryer, T. (2017) Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data. Calcolo, 54 (4). pp. 1533-1551. ISSN 1126-5434 doi: 10.1007/s10092-017-0240-5

Abstract/Summary

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control.

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Item Type Article
URI https://reading-clone.eprints-hosting.org/id/eprint/72701
Identification Number/DOI 10.1007/s10092-017-0240-5
Refereed Yes
Divisions Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher Springer
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