ON THE CONVERGENCE OF FINITE-ELEMENT APPROXIMATIONS OF A RELAXED VARIATIONAL PROBLEM

The accuracy of finite-element approximations to a convex, but not strictly convex, variational problem is considered. Convergence is proved for a finite-element approximation of a particular vector field related to the solution. In a special one-dimensional case, 0(h) convergence is shown for a piecewise linear approximation of the derivative. h denotes the size of each element domain. Numerical results are also presented for this one-dimensional case. The problem arises in the relaxation of an elastostatic antiplane shear problem with nonconvex energy.