A self-adaptive mesh refinement technique for boundary element solution of the Laplace equation.

1988 ◽  
Vol 3 (5) ◽  
pp. 309-319 ◽  
Author(s):  
J. J. Rencis ◽  
R. L. Mullen
Keyword(s):  
Boundary Element ◽  
Laplace Equation ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Element Solution ◽  
Self Adaptive

Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods

2013 ◽  
Vol 13 (3) ◽  
pp. 305-332 ◽  
Author(s):  
Markus Aurada ◽  
Michael Feischl ◽  
Thomas Führer ◽  
Michael Karkulik ◽  
Dirk Praetorius
Keyword(s):  
Boundary Element ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Weak Form ◽  
Adaptive Strategy ◽  
Optimal Choice ◽  
Residual Error ◽  
Boundary Element Methods ◽  
Error Estimator

Abstract. We prove convergence and quasi-optimality of a lowest-order adaptive boundary element method for a weakly-singular integral equation in 2D. The adaptive mesh-refinement is driven by the weighted-residual error estimator. By proving that this estimator is not only reliable, but under some regularity assumptions on the given data also efficient on locally refined meshes, we characterize the approximation class in terms of the Galerkin error only. In particular, this yields that no adaptive strategy can do better, and the weighted-residual error estimator is thus an optimal choice to steer the adaptive mesh-refinement. As a side result, we prove a weak form of the saturation assumption.

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