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

• Published in: Computers & mathematics with applications (1987) Vol. 76; no. 7; pp. 1639 - 1660
• Main Authors: Banz, Lothar, Lamichhane, Bishnu P., Stephan, Ernst P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2018; Elsevier BV
• Subjects: [formula omitted]-adaptive FEM; [formula omitted]-Laplacian obstacle problem; A posteriori error estimate; A priori error estimate; Boundary value problems; Convergence; Differential equations; Finite element analysis; Finite element method; Mathematical analysis; Operators (mathematics); Polynomials; p-Laplacian obstacle problem; A priori error estimate; A posteriori error estimate; hq-adaptive FEM
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2018.07.016

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.