Adaptive \(r\) and \(h-r\) algorithms for boundary elements (Q1803727)

Adaptive meshing is an important tool for the numerical solution of partial differential equations. The impact of adaptive meshing is particularly evident when dealing with severe nonlinearities arising in certain initial-boundary value problems. In this paper the techniques of mesh redistribution \((r)\) and mesh refinement-redistribution \((h-r)\) are proven to be of considerable practical importance in the numerical solution of boundary value problems. The implementation of these techniques in the boundary element formulation is considered. To assess the validity of the proposed algorithms, two model problems are employed. These problems are the potential equation and the equations of linear elasticity in two dimensions, both containing boundary singularities of crack type.