Analysis of an interface relaxation method for composite elliptic differential equations

The theoretical analysis on both the continuous (differential) and the discrete (linear algebra) levels of an interface relaxation method for solving elliptic differential equations is presented. The convergence of the method for 1-dimensional problems is proved. The region of convergence and the optimal values for the relaxation parameters involved are determined for model problems. Numerical data for 1- and 2-dimensional problems that confirm the theoretical results, exhibit the effectiveness of the method and elucidate its characteristics are presented.