Details
| Original language | English |
|---|---|
| Title of host publication | Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 |
| Subtitle of host publication | European Conference, September 4-8, Lisbon, Portugal |
| Editors | Adélia Sequeira, Ana Silvestre, Svilen S. Valtchev, João Janela |
| Pages | 340-349 |
| Number of pages | 10 |
| ISBN (electronic) | 978-3-031-86169-7 |
| Publication status | Published - 28 Apr 2025 |
| Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023 - Lisbon, Portugal Duration: 4 Sept 2023 → 8 Sept 2023 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering (LNCSE) |
|---|---|
| Volume | 154 |
| ISSN (Print) | 1439-7358 |
| ISSN (electronic) | 2197-7100 |
Abstract
We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, the main interest lies in an accurate computation of some possibly nonlinear functionals at the solution, so called goal functionals. This motivates the use of adaptive mesh refinements driven by the dual-weighted residual (DWR) method. The DWR method requires the numerical solution of a linear adjoint problem which provides information on where the error in the solution has the most influence on the goal functional. This can be done by means of the same full space-time finite element discretization as used for the primal linear problem. The numerical experiment presented demonstrates that this goal-oriented full space-time finite element solver efficiently provides accurate numerical results for a model problem with moving domains and a linear goal functional.
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- General Engineering
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Computational Mathematics
Cite this
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Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2: European Conference, September 4-8, Lisbon, Portugal. ed. / Adélia Sequeira; Ana Silvestre; Svilen S. Valtchev; João Janela. 1. ed. 2025. p. 340-349 (Lecture Notes in Computational Science and Engineering (LNCSE); Vol. 154).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Goal-Oriented Adaptive Space Time Finite Element Methods Applied to Touching Domains
AU - Endtmayer, Bernhard
AU - Schafelner, Andreas
N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025/4/28
Y1 - 2025/4/28
N2 - We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, the main interest lies in an accurate computation of some possibly nonlinear functionals at the solution, so called goal functionals. This motivates the use of adaptive mesh refinements driven by the dual-weighted residual (DWR) method. The DWR method requires the numerical solution of a linear adjoint problem which provides information on where the error in the solution has the most influence on the goal functional. This can be done by means of the same full space-time finite element discretization as used for the primal linear problem. The numerical experiment presented demonstrates that this goal-oriented full space-time finite element solver efficiently provides accurate numerical results for a model problem with moving domains and a linear goal functional.
AB - We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, the main interest lies in an accurate computation of some possibly nonlinear functionals at the solution, so called goal functionals. This motivates the use of adaptive mesh refinements driven by the dual-weighted residual (DWR) method. The DWR method requires the numerical solution of a linear adjoint problem which provides information on where the error in the solution has the most influence on the goal functional. This can be done by means of the same full space-time finite element discretization as used for the primal linear problem. The numerical experiment presented demonstrates that this goal-oriented full space-time finite element solver efficiently provides accurate numerical results for a model problem with moving domains and a linear goal functional.
UR - http://www.scopus.com/inward/record.url?scp=105004796444&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-86169-7_35
DO - 10.1007/978-3-031-86169-7_35
M3 - Conference contribution
AN - SCOPUS:105004796444
SN - 978-3-031-86168-0
SN - 978-3-031-86171-0
T3 - Lecture Notes in Computational Science and Engineering (LNCSE)
SP - 340
EP - 349
BT - Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2
A2 - Sequeira, Adélia
A2 - Silvestre, Ana
A2 - Valtchev, Svilen S.
A2 - Janela, João
T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023
Y2 - 4 September 2023 through 8 September 2023
ER -