- Title
- Higher order mixed FEM for the obstacle problem of the p-Laplace equation using biorthogonal systems
- Creator
- Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P.
- Relation
- Computational Methods in Applied Mathematics Vol. 19, Issue 2, p. 169-188
- Publisher Link
- http://dx.doi.org/10.1515/cmam-2018-0015
- Publisher
- Walter de Gruyter GmbH
- Resource Type
- journal article
- Date
- 2018
- Description
- We consider a mixed finite element method for an obstacle problem with the p-Laplace differential operator for p∈(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.
- Subject
- a priori error estimate; a posteriori error estimate; discrete Inf-Sup constant; 65N30; 65N15; 74M15; p-Laplace obstacle problem
- Identifier
- http://hdl.handle.net/1959.13/1417064
- Identifier
- uon:37156
- Identifier
- ISSN:1609-4840
- Language
- eng
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