Details
| Original language | English |
|---|---|
| Pages (from-to) | 1893-1926 |
| Number of pages | 34 |
| Journal | IMA Journal of Numerical Analysis |
| Volume | 38 |
| Issue number | 4 |
| Early online date | 28 Sept 2017 |
| Publication status | Published - Oct 2018 |
Abstract
We derive and analyse discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We present different symmetric and nonsymmetric formulations, where optimal test functions are used only for the partial differential equation part of the problem, not the boundary conditions. For the symmetric case and lowest-order approximations, we provide a simple a posteriori error estimate. In the second part, we apply our technique to the singularly perturbed case of reaction-dominated diffusion. Numerical results show the performance of our method and, in particular, its robustness in the singularly perturbed case.
Keywords
- contact problem, DPG method, optimal test functions, reaction-dominated diffusion, Signorini problem, ultra-weak formulation, variational inequality
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: IMA Journal of Numerical Analysis, Vol. 38, No. 4, 10.2018, p. 1893-1926.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the DPG method for Signorini problems
AU - Führer, Thomas
AU - Heuer, Norbert
AU - Stephan, Ernst P.
PY - 2018/10
Y1 - 2018/10
N2 - We derive and analyse discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We present different symmetric and nonsymmetric formulations, where optimal test functions are used only for the partial differential equation part of the problem, not the boundary conditions. For the symmetric case and lowest-order approximations, we provide a simple a posteriori error estimate. In the second part, we apply our technique to the singularly perturbed case of reaction-dominated diffusion. Numerical results show the performance of our method and, in particular, its robustness in the singularly perturbed case.
AB - We derive and analyse discontinuous Petrov-Galerkin methods with optimal test functions for Signorini-type problems as a prototype of a variational inequality of the first kind. We present different symmetric and nonsymmetric formulations, where optimal test functions are used only for the partial differential equation part of the problem, not the boundary conditions. For the symmetric case and lowest-order approximations, we provide a simple a posteriori error estimate. In the second part, we apply our technique to the singularly perturbed case of reaction-dominated diffusion. Numerical results show the performance of our method and, in particular, its robustness in the singularly perturbed case.
KW - contact problem
KW - DPG method
KW - optimal test functions
KW - reaction-dominated diffusion
KW - Signorini problem
KW - ultra-weak formulation
KW - variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85054364192&partnerID=8YFLogxK
U2 - 10.1093/imanum/drx048
DO - 10.1093/imanum/drx048
M3 - Article
AN - SCOPUS:85054364192
VL - 38
SP - 1893
EP - 1926
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
SN - 0272-4979
IS - 4
ER -