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Computational Methods in Applied Mathematics

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Higher Order Mixed FEM for the Obstacle Problem of the p-Laplace Equation Using Biorthogonal Systems

Lothar Banz / Bishnu P. Lamichhane
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  • School of Mathematical & Physical Sciences, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia
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/ Ernst P. Stephan
Published Online: 2018-06-21 | DOI: https://doi.org/10.1515/cmam-2018-0015


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.

Keywords: A Priori Error Estimate; A Posteriori Error Estimate; Discrete Inf-Sup Constant

MSC 2010: 65N30; 65N15; 74M15


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About the article

Received: 2017-12-12

Revised: 2018-04-30

Accepted: 2018-06-07

Published Online: 2018-06-21

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.

Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0015.

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