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Approximation Algorithms for Complex Systems pp 91–126Cite as

Discontinuous Galerkin Methods for Linear Problems: An Introduction

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Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 3))

Summary

Discontinuous Galerkin (dG) methods for the numerical solution of partial differential equations (PDE) have enjoyed substantial development in re- cent years. Possible reasons for this are the flexibility in local approximation they offer, together with their good stability properties when approximating convection- dominated problems. Owing to their interpretation both as Galerkin projections onto suitable energy (native) spaces and, simultaneously, as high order versions of classical upwind finite volume schemes, they offer a range of attractive properties for the numerical solution of various classes of PDE problems where classical fi- nite element methods under-perform, or even fail. These notes aim to be a gentle introduction to the subject.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, LE1 7RH, Leicester, UK

    Emmanuil H. Georgoulis

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  1. Emmanuil H. Georgoulis
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Editors and Affiliations

  1. , Dept. of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Emmanuil H Georgoulis

  2. Abt. Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Armin Iske

  3. Dept. Mathematics and, Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

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Georgoulis, E.H. (2011). Discontinuous Galerkin Methods for Linear Problems: An Introduction. In: Georgoulis, E., Iske, A., Levesley, J. (eds) Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16876-5_5

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