A discretization theory for a class of semi-coercive unilateral problems
The authors consider semi-coercive variational inequalities typical of contract problems in elasto-statics, statics, and their finite element approximation. They show that weak accumulation points of the sequence of finite element solutions are solutions of the original problem. As the solution does not have to be unique, not more can be expected. If on the other hand the original problem has a unique solution, we obtain strong convergence of the finite element solutions, as well as in the non-unique case the strong convergence of the regularised Tikhonov solutions towards the original solution of minimal norm. The results are demonstrated by some numerical examples.
scientific article; zbMATH DE number 1545475