Aplicação do método de elementos finitos e FDA-NCP em problemas de complementaridade

Abstract

A large number of problems in different disciplines lead to complementarity problems. This is the case of contact problems in Mechanics and the problem of oxygen diffusion in tissues, that is presented in this work. Many of these problems have analytical and numerical difficulties such as the determination of a moving boundary, which hinders their resolution. In this work we are considering complementarity problems that involves spatial coordinates. We propose a numerical strategy to solve this kind of problem based on the construction of variational formulations by using the finite element method. The FDA-NCP algorithm is used to solve the complementarity problems and, for time dependent models, we use an implicit finite difference scheme to obtain the discrete formulation. Although this approach is presented as a general technique, only a one-dimensional spatial problem is numerically solved in the present work. The numerical results obtained show agreement with some other results from previous works.