Interval Bounds on the Local Discretization Error in Boundary Element Analysis for Domains with Singular Flux

摘要

In engineering most partial differential equations are solved using numerical methods. Throughout the years finite element method emerged as the most widely used numerical technique to obtain discrete solutions to partial differential equations. An alternative method to the finite element method is the boundary element method. In boundary element formulation the domain variables are transformed to boundary variables using Green's functions of the partial differential equations. The uncertainty in the solutions to boundary values in boundary element method has been studied using interval approach. Interval treatment of the uncertainty in boundary conditions, integration, truncation, and discretization errors has been developed. In this work local discretization error is computed for the problems exhibiting singular flux. Example is shown demonstrating the behavior of the worst case bounds on the discretization error in the presence of singular solutions.