On the numerical analysis of a nonlinear elliptic problem via mixed-FEM and Lagrange multi\-pliers.
The paper deals with mixed finite elements for solving nonlinear second-order elliptic problems. The theoretical results extend previous ones with respect to stronger nonlinearities and mixed boundary conditions. Rigorous mathematical proofs show that the variational formulation and the associated discrete problem are well posed and a priori error estimates are derived. Also an a posteriori error analysis is provided which serves as the basis for adaptive grid refinement. Numerical results for two simple test cases are presented which confirm the theoretical results. In particular, a comparison with computations with uniform refinement illustrate the advantages of the adaptive approach.
nonlinear second-order elliptic problems
scientific article; zbMATH DE number 2055525
scientific article