A multilevel algorithm for the solution of second order elliptic differential equations on sparse grids

Abstract

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles in \(x\)- and \(y\)-direction. A suitable discretization provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order \(O(1)\) for the multilevel algorithm.