Anisotropic hp-mesh optimization technique based on the continuous mesh and error models
Result description
We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the hp-version of the finite element method (hp-FEM). The technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees. We present a hp-version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem. Solving the optimization problem leads to hp-mesh with the smallest number of degrees of freedom, under the constraint that the approximate solution has an error estimate below a given tolerance. Further, we propose an iterative algorithm to find a suitable anisotropic hp-mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.
Keywords
Mesh optimizationContinuous error modelContinuous mesh modelAnisotropic mesh adaptationhp-methods
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Anisotropic hp-mesh optimization technique based on the continuous mesh and error models
Original language description
We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the hp-version of the finite element method (hp-FEM). The technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees. We present a hp-version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem. Solving the optimization problem leads to hp-mesh with the smallest number of degrees of freedom, under the constraint that the approximate solution has an error estimate below a given tolerance. Further, we propose an iterative algorithm to find a suitable anisotropic hp-mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computers and Mathematics with Applications
ISSN
0898-1221
e-ISSN
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Volume of the periodical
74
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
19
Pages from-to
45-63
UT code for WoS article
000403633600005
EID of the result in the Scopus database
2-s2.0-85008608257
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2017