Adaptive Wavelet BEM for Boundary Integral Equations: Theory and Numerical Experiments

ABSTRACT

We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in ℝ³. The corresponding operator equations are treated by adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions based on the Besov regularity of the exact solution.

KEYWORDS:

• Adaptive wavelet BEM
• Besov spaces
• double layer potential operator
• integral equations
• manifolds
• non-linear approximation
• regularity
• weighted Sobolev spaces

AMS SUBJECT CLASSIFICATION:

• 30H25
• 35B65
• 42C40
• 45E99
• 46E35
• 47B38
• 65T60