An approximation of anisotropic metrics from higher order interpolation error for triangular mesh adaptation

Hecht, Frédéric; Kuate, Raphaël

doi:10.1016/j.cam.2013.09.002

Cited by 9 publications

(2 citation statements)

References 16 publications

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“…The key point is to be able to e ciently reduce the multi-linear form that occurs in such a formulation into a bilinear one in order to apply the continuous mesh framework. With straight elements, a metric-based control of the interpolation error is studied in [134,135] in 2D. In 3D, only a few works exist.…”

Section: High-order Adapted Meshesmentioning

confidence: 99%

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

Alauzet

Loseille

2016

Computer-Aided Design

156

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Please cite this article as: Alauzet F, Loseille A. A decade of progress on anisotropic mesh adaptation for computational fluid dynamics. Computer-Aided Design (2015), http://dx. AbstractIn the context of scientific computing, the mesh is used as a discrete support for the considered numerical methods. As a consequence, the mesh greatly impacts the e ciency, the stability and the accuracy of numerical methods. The goal of anisotropic mesh adaptation is to generate a mesh which fits the application and the numerical scheme in order to achieve the best possible solution. It is thus an active field of research which is progressing continuously. This review article proposes a synthesis of the research activity of the INRIA Gamma3 team in the field of anisotropic mesh adaptation applied to inviscid flows in computational fluid dynamics since 2000. It shows the evolution of the theoretical and numerical results during this period. Finally, challenges for the next decade are discussed.

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Section: High-order Adapted Meshesmentioning

confidence: 99%

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

Alauzet

Loseille

2016

Computer-Aided Design

156

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“…Concentrating on test examples of colloidal particles in confined nematic matrix (shortly, confined nematic colloids), which present a challenging, almost singular behaviour regarding mesh resolution requirements, the hereby presented scheme makes use of the mesh adaptivity tool of metric mappings, or shorter just metrics. These are representing a posteriori error estimates based on the Hessian of the solution(s), and are a still evolving [17] subfield of mesh adaptivity.…”

Section: Introductionmentioning

confidence: 99%

A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency

Bajc

Hecht

Žumer

2016

Journal of Computational Physics

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International audienceThis paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics derived from the Hessian of a solution. The study is made on the case of a nonlinear finite element minimization scheme for the Landau–de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in

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Optimally Convergent Isoparametric $$P^2$$ Mesh Generation

Bawin,

Garon,

Remacle

2024

Lecture Notes in Computational Science and Engineering

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An approximation of anisotropic metrics from higher order interpolation error for triangular mesh adaptation

Cited by 9 publications

References 16 publications

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

A mesh adaptivity scheme on the Landau–de Gennes functional minimization case in 3D, and its driving efficiency

Optimally Convergent Isoparametric $$P^2$$ Mesh Generation

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