Details
| Original language | English |
|---|---|
| Pages (from-to) | 1679-1718 |
| Number of pages | 40 |
| Journal | Numerische Mathematik |
| Volume | 156 |
| Issue number | 5 |
| Early online date | 25 Sept 2024 |
| Publication status | Published - Oct 2024 |
Abstract
An hp-finite element discretization for the α-Mosolov problem, a scalar variant of the Bingham flow problem but with the α-Laplacian operator, is being analyzed. Its weak formulation is either a variational inequality of second kind or equivalently a non-smooth but convex minimization problem. For any α∈(1,∞) we prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the FE-solution of the corresponding discrete variational inequality. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. We prove that any quasi-minimizer of those families of a posteriori error estimators satisfies an efficiency estimate. All our results contain known results for the Mosolov problem by setting α=2. Numerical results underline our theoretical findings.
Keywords
- 65K15, 65N30, 65N50
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerische Mathematik, Vol. 156, No. 5, 10.2024, p. 1679-1718.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - hp-FEM for the α-Mosolov problem
T2 - a priori and a posteriori error estimates
AU - Banz, Lothar
AU - Stephan, Ernst P.
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/10
Y1 - 2024/10
N2 - An hp-finite element discretization for the α-Mosolov problem, a scalar variant of the Bingham flow problem but with the α-Laplacian operator, is being analyzed. Its weak formulation is either a variational inequality of second kind or equivalently a non-smooth but convex minimization problem. For any α∈(1,∞) we prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the FE-solution of the corresponding discrete variational inequality. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. We prove that any quasi-minimizer of those families of a posteriori error estimators satisfies an efficiency estimate. All our results contain known results for the Mosolov problem by setting α=2. Numerical results underline our theoretical findings.
AB - An hp-finite element discretization for the α-Mosolov problem, a scalar variant of the Bingham flow problem but with the α-Laplacian operator, is being analyzed. Its weak formulation is either a variational inequality of second kind or equivalently a non-smooth but convex minimization problem. For any α∈(1,∞) we prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the FE-solution of the corresponding discrete variational inequality. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. We prove that any quasi-minimizer of those families of a posteriori error estimators satisfies an efficiency estimate. All our results contain known results for the Mosolov problem by setting α=2. Numerical results underline our theoretical findings.
KW - 65K15
KW - 65N30
KW - 65N50
UR - http://www.scopus.com/inward/record.url?scp=85204783311&partnerID=8YFLogxK
U2 - 10.1007/s00211-024-01433-8
DO - 10.1007/s00211-024-01433-8
M3 - Article
AN - SCOPUS:85204783311
VL - 156
SP - 1679
EP - 1718
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 5
ER -