Enclosure of solutions of weakly nonlinear elliptic boundary value problems and their computation
An algorithm is presented to compute approximate as well as continuous bounds for solutions of weakly nonlinear elliptic boundary value problems. The given problem is majorized in some sense and the resulting problem is solved by a finite element method. The finite element solution is computed by a monotone iteration process and finally transformed into a continuous (lower) bound for a solution. Convergence is proved and the effects of mesh refinement are discussed. Two numerical examples are given.
weakly nonlinear elliptic boundary value problems
scientific article; zbMATH DE number 4115884
scientific article