An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472960" target="_blank" >RIV/00216208:11320/23:10472960 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=whj~QRTvzE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=whj~QRTvzE</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10915-023-02153-1" target="_blank" >10.1007/s10915-023-02153-1</a>
Alternative languages
Result language
angličtina
Original language name
An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control
Original language description
We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder Omega x (0, T). We employ the space-time discontinuous Galerkin method which enables us to use different meshes at different time levels in a natural way. The mesh adaptive algorithm is based on control of the interpolation error in the L-infinity(0, T; L-q(Omega))-norm. The goal is to construct a sequence of conforming triangular meshes in such a way that the interpolation error bound is under a given tolerance and the number of degrees of freedom is minimal. The resulting grids consist of anisotropic mesh elements with varying polynomial approximation degrees with respect to space. We present a theoretical framework of this approach as well as several numerical examples demonstrating the accuracy, efficiency, and applicability of the method.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Scientific Computing
ISSN
0885-7474
e-ISSN
1573-7691
Volume of the periodical
95
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
31
Pages from-to
36
UT code for WoS article
000953450400004
EID of the result in the Scopus database
2-s2.0-85150806238