Dual boundary-element method: Simple error estimator and adaptivity.

This paper is concerned with the effective numerical implementation of the adaptive dual boundary-element method (DBEM), for two-dimensional potential problems. Two boundary integral equations, which are the potential and the flux equations, are applied for collocation along regular and degenerate boundaries, leading always to a single-region analysis. Taking advantage on the use of nonconforming parametric boundary-elements, the method introduces a simple error estimator, based on the discontinuity of the solution across the boundaries between adjacent elements and implements the p, h and mixed versions of the adaptive mesh refinement. Examples of several geometries, which include degenerate boundaries, are analyzed with this new formulation to solve regular and singular problems. The accuracy and efficiency of the implementation described herein make this a reliable formulation of the adaptive DBEM.