Higher order FEM for the obstacle problem of the p-Laplacian—A variational inequality approach

We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the poly...

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Published inComputers & mathematics with applications (1987) Vol. 76; no. 7; pp. 1639 - 1660
Main Authors Banz, Lothar, Lamichhane, Bishnu P., Stephan, Ernst P.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.10.2018
Elsevier BV
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Summary:We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.07.016