Abstract

An anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented. The procedure is applied to transient 2- and 3-dimensional problems governed by Euler’s equation. A smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified. The mesh metric field in smooth portions of the domain is controlled by a Hessian matrix constructed using a variational procedure to calculate the second derivatives. The transient examples included demonstrate the ability of the mesh modification procedures to effectively track evolving interacting features of general shape as they move through a domain. Copyright c 2000 John Wiley & Sons, Ltd. KEY WORDS: anisotropic adaptive, discontinuous Galerkin, mesh modification

Keywords

DiscretizationTransient (computer programming)Finite element methodHessian matrixSmoothnessGalerkin methodIsogeometric analysisDiscontinuous Galerkin methodMesh generationMetric (unit)MathematicsApplied mathematicsMetric tensorDomain (mathematical analysis)Computer scienceMathematical analysisAlgorithmEngineeringStructural engineering

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Publication Info

Year
2004
Type
article
Volume
62
Issue
7
Pages
899-923
Citations
95
Access
Closed

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Jean‐François Remacle, Xiangrong Li, Mark S. Shephard et al. (2004). Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. International Journal for Numerical Methods in Engineering , 62 (7) , 899-923. https://doi.org/10.1002/nme.1196

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DOI
10.1002/nme.1196