Numerical verification of solutions for variational inequalities
The paper deals with the study of a numerical technique that enables to verify the existence of solutions for variational inequalities. This technique is based on the infinite-dimensional fixed point theorems and explicit error estimates for finite element approximations. Main result: A new method which automatically proves the existence of weak solutions for variational inequalities by numerical computation (the basis of given method consists of computing procedures to verify the existence and inclusion set of a solution by using Schauder's fixed point theorem), is described. Due to the finite element approximations and explicit a priori error estimates for obstacle problems, the authors present an effective verification procedure that through numerical computation generates a set, which includes the exact solution. Finally, a numerical example for an obstacle problem is presented.
scientific article; zbMATH DE number 1247607