C. Carstensen, D. Praetorius:

"A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind";

SIAM Journal on Scientific Computing,25(2004), 1; 259 - 283.

Sobolev-Slobodeckij norms on small overlapping domains of two

neighbouring elements serve as a~posteriori error estimators and

mesh-refining indicators in adaptive boundary element methods.

The paper is concerned with two error estimators $\eta_F$ and $\mu_F$.

The first variant $\eta_F$ is efficient and the second $\mu_F$ is reliable,

that is, up to multiplicative constants and numerical quadrature

errors, they are lower or upper error bounds.

Faermann recently established reliability and efficiency

of $\eta_F$ for the Galerkin boundary element method and

considered $\mu_F$.

This work approaches the two estimators $\eta_F\le\mu_F$ for

the Galerkin, qualocation, and collocation boundary element methods

for a single layer operator integral equation of the first kind.

Upper and lower bounds are established theoretically and validated

numerically. Numerical experiments support the estimators' accuracies

and the efficiencies of proposed adaptive mesh-refining algorithms

even in energy norms. For qualocation and collocation schemes,

difficulties for $\alpha\le 1/2$ are caused by the lack of a

Sobolev embedding $H^\alpha(\Gamma)\hookrightarrow\CC(\Gamma)$.

Hence, for the latter schemes, equivalence of error and estimators in

$H^{\alpha-1}(\Gamma)$ can be proven only for $\alpha>1/2$. Numerical

evidence conjectures equivalence for $\alpha=1/2$ as well.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04969697

http://www.anum.tuwien.ac.at/~dirk/download/published/ccdpr01_sisc25.pdf

Created from the Publication Database of the Vienna University of Technology.