On the Rate of Convergence of the Bergman-Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems - Eisenstat, Stanley C. (SIAM journal on numerical analysis, 1974)
We consider the Bergman-Vekua method of particular solutions for the numerical solution of elliptic boundary value problems. The rate of convergence is shown to depend on the smoothness of the solution or, equivalently for domains with smooth boundary, on the smoothness of the boundary data. For domains with piecewise smooth boundary, the introduction of certain singular particular solutions is shown to lead to a similar dependency. A method for solving the membrane eigenvalue problem is proposed and shown to have the same rate of convergence.