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Ženíšek, Alexander

The finite element method for nonlinear elliptic equations with discontinuous coefficients. (English) Zbl 0709.65081

Numer. Math. 58, No. 1, 51-77 (1990).
The study of the finite element approximation to nonlinear second order elliptic boundary value problems with discontinuous coefficients is presented in the case of mixed Dirichlet-Neumann boundary conditions. The change in domain and numerical integration are taken into account. With the assumptions which guarantee that the corresponding operator is strongly monotone and Lipschitz-continuous the following convergence results are proved: 1. The rate of convergence \(O(h^{\epsilon})\) if the exact solution \(u\in H^ 1(\Omega)\) is piecewise of class \(H^{1+\epsilon}\) \((0<\epsilon \leq 1)\); 2. The convergence without any rate of convergence if \(u\in H^ 1(\Omega)\) only.
Reviewer: Jiping Lu

Cited in 28 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations

Keywords:

finite element; nonlinear second order elliptic boundary value problems; discontinuous coefficients; mixed Dirichlet-Neumann boundary conditions; convergence
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References:

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