## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 286-297 |

Seitenumfang | 12 |

Fachzeitschrift | Computers and Mathematics with Applications |

Jahrgang | 167 |

Frühes Online-Datum | 31 Mai 2024 |

Publikationsstatus | Veröffentlicht - 1 Aug. 2024 |

## Abstract

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals.

## ASJC Scopus Sachgebiete

- Mathematik (insg.)
**Modellierung und Simulation**- Informatik (insg.)
**Theoretische Informatik und Mathematik**- Mathematik (insg.)
**Computational Mathematics**

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**Goal-oriented adaptive space-time finite element methods for regularized parabolic p-Laplace problems.**/ Endtmayer, B.; Langer, U.; Schafelner, A.

in: Computers and Mathematics with Applications, Jahrgang 167, 01.08.2024, S. 286-297.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Computers and Mathematics with Applications*, Jg. 167, S. 286-297. https://doi.org/10.48550/arXiv.2306.07167, https://doi.org/10.1016/j.camwa.2024.05.017

*Computers and Mathematics with Applications*,

*167*, 286-297. https://doi.org/10.48550/arXiv.2306.07167, https://doi.org/10.1016/j.camwa.2024.05.017

}

TY - JOUR

T1 - Goal-oriented adaptive space-time finite element methods for regularized parabolic p-Laplace problems

AU - Endtmayer, B.

AU - Langer, U.

AU - Schafelner, A.

N1 - Publisher Copyright: © 2024 The Author(s)

PY - 2024/8/1

Y1 - 2024/8/1

N2 - We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals.

AB - We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals.

KW - Goal-oriented adaptivity

KW - Regularized parabolic p-Laplacian

KW - Space-time finite element discretization

UR - http://www.scopus.com/inward/record.url?scp=85194583611&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2306.07167

DO - 10.48550/arXiv.2306.07167

M3 - Article

AN - SCOPUS:85194583611

VL - 167

SP - 286

EP - 297

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -