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Anisotropic hp-Mesh adaptation methodstheory, implementation and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Anisotropic hp-Mesh adaptation methodsby Vit Dolejsi, Georg May.
Reminder of title:	theory, implementation and applications /
Author:	Dolejsi, Vit.
other author:	May, Georg.
Published:	Cham :Springer International Publishing :2022.
Description:	x, 252 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, PartialNumerical solutions.
Online resource:	https://doi.org/10.1007/978-3-031-04279-9
ISBN:	9783031042799$q(electronic bk.)

Anisotropic hp-Mesh adaptation methodstheory, implementation and applications /
Dolejsi, Vit.

Anisotropic hp-Mesh adaptation methodstheory, implementation and applications /[electronic resource] :by Vit Dolejsi, Georg May. - Cham :Springer International Publishing :2022. - x, 252 p. :ill., digital ;24 cm. - Necas Center series,2523-3351. - Necas Center series..

Introduction -- Metric Based Mesh Representation -- Interpolation Error Estimates for Two Dimensions -- Interpolation Error Estimates for Three Dimensions -- Anisotropic Mesh Adaptation, h-Variant -- Anisotropic Mesh Adaptation Method, hp-Variant -- Framework of the Goal-Oriented Error Estimates -- Goal-Oriented Anisotropic Mesh Adaptation -- Implementation Aspects -- Applications.

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

ISBN: 9783031042799$q(electronic bk.)

Standard No.: 10.1007/978-3-031-04279-9doiSubjects--Topical Terms:

185034
Differential equations, Partial
--Numerical solutions.

LC Class. No.: QA377 / .D65 2022

Dewey Class. No.: 518.64

Anisotropic hp-Mesh adaptation methodstheory, implementation and applications /
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505 0 $a Introduction -- Metric Based Mesh Representation -- Interpolation Error Estimates for Two Dimensions -- Interpolation Error Estimates for Three Dimensions -- Anisotropic Mesh Adaptation, h-Variant -- Anisotropic Mesh Adaptation Method, hp-Variant -- Framework of the Goal-Oriented Error Estimates -- Goal-Oriented Anisotropic Mesh Adaptation -- Implementation Aspects -- Applications.
520 $a Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.
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