Nonlinear SOR and mesh redistribution

This article concerns the numerical approximations for the problems of minimizing strict convex functionals. The functionals are discretized by the finite-element methods and then solved by the nonlinear SOR with an optimal mesh. The redistribution approach is considered to generate the optimal mesh. With an optimal mesh, the number of unknowns can be dramatically reduced and this generally gives a computationally efficient model. Numerical results of the model catenoid problem and a geodesics problem illustrating the efficiency of the optimal mesh approach in the nonlinear SOR will be presented.