The work at hand is devoted to the numerical treatment of systems of partial differential equations, where the solution is subjected to inequality constraints. We employ the finite element Galerkin (FE) method to obtain approximate solutions of such systems, which for instance typically arise in the field of continuum mechanics. Examples are plastic materials, where certain norms of the stresses are bounded or contact problems, where the displacement is restricted by a rigid obstacle. For illustration, the situation of a workpiece pressed onto a grinding disk (Figures 1.1, 1.2 is approximated by a FE-scheme (Figures 1.3, 1.4) to approximate the resulting surface forces. The basis for applying an FE discretisation is a suitable mathematical setting, which in the topics under consideration takes the form of variational inequalities (VI).
KeywordsVariational Inequality Posteriori Error Model Situation Obstacle Problem Posteriori Error Estimate
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