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

Title: Higher order FEM for the obstacle problem of the p-Laplacian—A variational inequality approach
Creator: Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P.
Relation: Computers and Mathematics with Applications Vol. 76, Issue 7, p. 1639-1660
Publisher Link: http://dx.doi.org/10.1016/j.camwa.2018.07.016
Publisher: Elsevier
Resource Type: journal article
Date: 2018
Description: 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.
Subject: p-Laplacian obstacle problem; a priori error estimate; a posteriori error estimate; hq-adaptive FEM
Identifier: http://hdl.handle.net/1959.13/1454403
Identifier: uon:44927
Identifier: ISSN:0898-1221
Language: eng
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