A posteriori error control in adaptive qualocation boundary element analysis for a logarithmic-kernel integral equation of the first kind. (English) Zbl 1042.65084
This study investigates a posteriori error estimators that are used in adaptive boundary element methods. The estimators are based on Sobolev-Slobodeckij norms on small overlapping domains of boundary elements. Two estimators are considered and their efficiency and reliability is investigated. Lower and upper bounds are derived theoretically and then confirmed by numerical experiments.
Reviewer: Nicolae S. Mera (Leeds)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65R20 | Numerical methods for integral equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
