Dual boundary‐element method: Simple error estimator and adaptivity

Abstract

SUMMARYThis 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 non-conforming 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.

Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

“…The method is called dual boundary element method (DBEM) [21]. DBEM provides an ecient way to model cracks of arbitrary 1D and 2D geometries [22][23] [7] [24]. Another approach is known as the displacement discontinuity method (DDM) [25], which is mostly suitable for problems with symmetry.…”

Refinamento adaptativo tipo H aplicado à formulação de elasticidade plana do método dos elementos de contorno dual

“…As normas representam a exatidão com que as variáveis de estado são modeladas pelos elementos de contorno, e são usadas para associar as estimativas dos respectivos erros de discretização(54). As normas são computadas como um somatório sobre todos os elementos do contorno.…”