Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics

In [13], a nonlinear elliptic equation arising from elastic-plastic mechanics is studied. A well-posed weak formulation is established for the equation and some regularity results are further obtained for the solution of the boundary problem. In this work, the finite element approximation of this boundary problem is examined in the framework of [13]. Some error bounds for this approximation are initially established in an energy type quasi-norm, which naturally arises in degenerate problems of this type and proves very useful in deriving sharper error bounds for the finite element approximation of such problems. For sufficiently regular solutions optimal error bounds are then obtained for some fully degenerate cases in energy type norms.