Finite element approximation of the volume-matching problem

Summary Optimal orderH¹ andL error bounds are obtained for a continuous piecewise linear finite element approximation of the volume matching problem. This problem consists of minimising |v|_1,² overvH¹() subject to the inequality constraintv0 and a number of linear equality constraints. The presence of the equality constraints leads to Lagrange multipliers, which in turn lead to complications with the standard error analysis for variational inequalities. Finally we consider an algorithm for solving the resulting algebraic problem.Supported by a SERC research studentship