Galerkin finite element methods for semilinear elliptic differential inclusions
In this paper we consider Galerkin finite element discretizations of semilinear elliptic differential inclusions that satisfy a relaxed one-sided Lipschitz condition. The properties of the set-valued Nemytskii operators are discussed, and it is shown that the solution sets of both, the continuous and the discrete system, are nonempty, closed, bounded, and connected sets in H-1-norm. Moreover, the solution sets of the Galerkin inclusion converge with respect to the Hausdorff distance measured in L-p-spaces.
18
2
295-312
295-312
American Institute Of Mathematical Sciences (Aims)