h--Adaptive mesh refinement strategy for the boundary element method based on local error analysis

摘要

An adaptive mesh refinement technique of the h type is proposed for the boundary element method (BEM). Error indicators at element level are evaluated based on a collocation scheme using ad hoc uniform norms that compare values of the field variables at successive iterations. Different approaches are applied depending on whether the boundary conditions are of the Neumann, Dirichlet, or Dirichlet- Neumann mixed type. For Neumann problems the error norms are evaluated using the standard discretised boundary integral equation (DBIE). Dirichlet problems are approached using both the standard DBIE and the hypersingular DBIE. Mixed problems are treated depending on the type of boundary condition. The technique is illustrated with examples for two-dimensional potential problems governed by the Laplace equation.