Numerical solutions of the m-membranes problem

In this paper numerical approximation for the m-membrane problem is considered. We make a change of variables that leads to a different expression of the quadratic functional that allows after discretizing the problem to reformulate it as finite dimensional bound constrained quadratic problem. To our knowledge this is the first paper on numerical approximation of the m-membrane problem. We reformulate the m-membrane problem as a bound constraint quadratic minimization problem. The bound constraint quadratic form is solved with the gradient projection method.

Research highlights
► We describe numerical approximation for the m-membranes problem.
► The original m-membranes problem is equivalent to the functional’s minimization over the same set.
► The problem expressed in displacements u can be reformulated in terms of u-differences.
► The finite dimensional version of bound constrained minimization problem written as a quadratic form.
► This problem can be solved with different methods, for numerical experiments gradient projection method is used.