An error estimation of a solution using the integral equation method

Some numerical experiments on estimating errors in a solution using the integral equation method are discussed. The new error estimating method can be used to evaluate a local error of the solution as well as the global error of the entire solution using an average. A performance index of the error is introduced that uses the integral equation itself and it is examined in a simple 3-D Laplace problem which has several kinds of nonuniform boundary mesh. The experimental results show that the index gives a good estimation of the margin of error and that it uniformly converges with respect to the number of elements (nodal points)