Details
| Original language | English |
|---|---|
| Pages (from-to) | 169-188 |
| Number of pages | 20 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 19 |
| Issue number | 2 |
| Early online date | 21 Jun 2018 |
| Publication status | Published - 1 Apr 2019 |
Abstract
We consider a mixed finite element method for an obstacle problem with the p-Laplace differential operator for p ϵ (1, ∞), where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the point-wise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (mesh-size adaptivity with and without polynomial degree adaptation) for the singular case p = 1.5 and the degenerated case p = 3. We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete inf-sup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.
Keywords
- A Posteriori Error Estimate, A Priori Error Estimate, Discrete Inf-Sup Constant, hq-Adaptive Mixed FEM, p-Laplace Obstacle Problem
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational Methods in Applied Mathematics, Vol. 19, No. 2, 01.04.2019, p. 169-188.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Higher Order Mixed FEM for the Obstacle Problem of the p-Laplace Equation Using Biorthogonal Systems
AU - Banz, Lothar
AU - Lamichhane, Bishnu P.
AU - Stephan, Ernst P.
N1 - Funding information: The visit of the third author to the University of Newcastle, Australia was partially supported by the priority research centre of the University of Newcastle for Computer-Assisted Research Mathematics and its Applications.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We consider a mixed finite element method for an obstacle problem with the p-Laplace differential operator for p ϵ (1, ∞), where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the point-wise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (mesh-size adaptivity with and without polynomial degree adaptation) for the singular case p = 1.5 and the degenerated case p = 3. We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete inf-sup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.
AB - We consider a mixed finite element method for an obstacle problem with the p-Laplace differential operator for p ϵ (1, ∞), where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the point-wise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (mesh-size adaptivity with and without polynomial degree adaptation) for the singular case p = 1.5 and the degenerated case p = 3. We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete inf-sup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.
KW - A Posteriori Error Estimate
KW - A Priori Error Estimate
KW - Discrete Inf-Sup Constant
KW - hq-Adaptive Mixed FEM
KW - p-Laplace Obstacle Problem
UR - http://www.scopus.com/inward/record.url?scp=85049129510&partnerID=8YFLogxK
U2 - 10.1515/cmam-2018-0015
DO - 10.1515/cmam-2018-0015
M3 - Article
AN - SCOPUS:85049129510
VL - 19
SP - 169
EP - 188
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
SN - 1609-4840
IS - 2
ER -