Adaptive Refinements in BEM

Abstract

Accuracy estimates and adaptive refinements is nowadays one of the main research topics in finite element computations [6,7,8, 9,11].Its extension to Boundary Elements has been tried as a means to better understand its capabilities as well as to impro ve its efficiency and its obvious advantages. The possibility of implementing adaptive techniques was shown [1,2] for h-conver gence and p-convergence respectively. Some posterior works [3,4 5,10] have shown the promising results that can be expected from those techniques. The main difficulty is associated to the reasonable establishment of “estimation” and “indication” factors related to the global and local errors in each refinement. Although some global measures have been used it is clear that the reduction in dimension intrinsic to boundary elements (3D→2D: 2D→1D) could allow a direct comparison among residuals using the graphic possibilities of modern computers and allowing a point-to-point comparison in place of the classical global approaches. Nevertheless an indicator generalizing the well known Peano’s one has been produced.