Adjoint error estimation and adaptivity for hyperbolic problems
In this article we present an overview of a posteriori error estimation and adaptive mesh design for hyperbolic/nearly-hyperbolic problems. In particular, we discuss the question of error estimation for general target functionals of the solution; typical examples include the outflow flux, local aver...
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| Format: | Book Section |
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Elsevier / North Holland
2017
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| Online Access: | https://eprints.nottingham.ac.uk/33969/ |
| _version_ | 1848794745580552192 |
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| author | Houston, Paul |
| author2 | Abgrall, Remi |
| author_facet | Abgrall, Remi Houston, Paul |
| author_sort | Houston, Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we present an overview of a posteriori error estimation and adaptive mesh design for hyperbolic/nearly-hyperbolic problems. In particular, we discuss the question of error estimation for general target functionals of the solution; typical examples include the outflow flux, local average and pointwise value, as well as the lift and drag coefficients of a body immersed in an inviscid fluid. By employing a duality argument weighted Type I and unweighted Type II bounds may be established. Here, the relative advantages of these two approaches are discussed in detail, together with the construction of appropriate dual problems that ensure optimality of the resulting bounds. The exploitation of general adaptive refinement strategies based on employing isotropic and anisotropic h- and hp-refinement will be discussed. Applications of this general theory to eigenvalue problems and bifurcation problems will also be presented. |
| first_indexed | 2025-11-14T19:21:05Z |
| format | Book Section |
| id | nottingham-33969 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:21:05Z |
| publishDate | 2017 |
| publisher | Elsevier / North Holland |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-339692020-05-04T18:29:13Z https://eprints.nottingham.ac.uk/33969/ Adjoint error estimation and adaptivity for hyperbolic problems Houston, Paul In this article we present an overview of a posteriori error estimation and adaptive mesh design for hyperbolic/nearly-hyperbolic problems. In particular, we discuss the question of error estimation for general target functionals of the solution; typical examples include the outflow flux, local average and pointwise value, as well as the lift and drag coefficients of a body immersed in an inviscid fluid. By employing a duality argument weighted Type I and unweighted Type II bounds may be established. Here, the relative advantages of these two approaches are discussed in detail, together with the construction of appropriate dual problems that ensure optimality of the resulting bounds. The exploitation of general adaptive refinement strategies based on employing isotropic and anisotropic h- and hp-refinement will be discussed. Applications of this general theory to eigenvalue problems and bifurcation problems will also be presented. Elsevier / North Holland Abgrall, Remi Shu, Chi-Wang 2017-01-30 Book Section PeerReviewed Houston, Paul (2017) Adjoint error estimation and adaptivity for hyperbolic problems. In: Handbook of Numerical Methods for Hyperbolic Problems. Applied and Modern Issues. Handbook of numerical analysis (18). Elsevier / North Holland, pp. 233-261. ISBN 9780444639103 Hyperbolic conservation laws adjoint methods adaptivity |
| spellingShingle | Hyperbolic conservation laws adjoint methods adaptivity Houston, Paul Adjoint error estimation and adaptivity for hyperbolic problems |
| title | Adjoint error estimation and adaptivity for hyperbolic problems |
| title_full | Adjoint error estimation and adaptivity for hyperbolic problems |
| title_fullStr | Adjoint error estimation and adaptivity for hyperbolic problems |
| title_full_unstemmed | Adjoint error estimation and adaptivity for hyperbolic problems |
| title_short | Adjoint error estimation and adaptivity for hyperbolic problems |
| title_sort | adjoint error estimation and adaptivity for hyperbolic problems |
| topic | Hyperbolic conservation laws adjoint methods adaptivity |
| url | https://eprints.nottingham.ac.uk/33969/ |