Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10225879 | Computers & Mathematics with Applications | 2018 | 22 Pages |
Abstract
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 pâ(1,â). 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Lothar Banz, Bishnu P. Lamichhane, Ernst P. Stephan,