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Robust DPG Methods for Transient Convection-Diffusion

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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 114))

Abstract

We introduce two robust DPG methods for transient convection-diffusion problems. Once a variational formulation is selected, the choice of test norm critically influences the quality of a particular DPG method. It is desirable that a test norm produce convergence of the solution in a norm equivalent to L 2 while producing optimal test functions that can be accurately computed and maintaining good conditioning of the optimal test function solve on highly adaptive meshes. Two such robust norms are introduced and proven to guarantee close to L 2 convergence of the primary solution variable. Numerical experiments demonstrate robust convergence of the two methods.

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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 East 24th St, Stop C0200, Austin, TX, 78712, USA

    Truman Ellis & Leszek Demkowicz

  2. Department of Mathematics, Virginia Tech, 460 McBryde Hall, Virginia Tech 225 Stanger Street, Blacksburg, VA, 24061-0123, USA

    Jesse Chan

Authors
  1. Truman Ellis
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  2. Jesse Chan
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  3. Leszek Demkowicz
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Corresponding author

Correspondence to Leszek Demkowicz .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Strathclyde, Glasgow, United Kingdom

    Gabriel R. Barrenechea

  2. Istituto di Matematica Applicata e Tecnologie Informatiche - Pavia, Consiglio Nazionale delle Ricerche, Pavia, Italy

    Franco Brezzi

  3. Department of Mathematics, University of Leicester, Leicester, United Kingdom

    Andrea Cangiani

  4. Department of Mathematics, National Technical University of Athens, Zografou, Greece

    Emmanuil H. Georgoulis

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Ellis, T., Chan, J., Demkowicz, L. (2016). Robust DPG Methods for Transient Convection-Diffusion. In: Barrenechea, G., Brezzi, F., Cangiani, A., Georgoulis, E. (eds) Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-41640-3_6

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