Order of convergence of the finite element method for the \(p(x)\)-Laplacian. (English) Zbl 1334.65181
The rate of convergence of the finite element method for the Dirichlet problem for the \(p(x)\)-Laplacian \((1\leq p_1\leq p(x)\leq p_2\leq 2)\) in a two-dimensional convex domain \(\Omega\) with Lipschitz boundary is studied. The paper is organized as follows. Section 1 is an introduction. In Section 2, some preliminary facts are given. The main results are proved in Section 3. A family of numerical examples is given in Section 4. When the decomposition-coordination method for approximating the solution is used, the behavior of the error is studied.
Reviewer: Temur A. Jangveladze (Tbilisi)
MSC:
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
65N15 | Error bounds for boundary value problems involving PDEs |