Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement (Q2864606)

The authors extend the 1D local approximation estimates for nodal interpolation to certain quasi-interpolation operators in 2D. Thus, they transfer the approximation properties of quasi-interpolation operators on adaptive meshes to positive fractional-order Sobolev spaces. Then they show that the discrete solutions provided by the introduced adaptive algorithm converge to the exact solution. The algorithm resolves possible singularities of the solution as well as of the given data. Some numerical experiments are carried out in order to underline that the sequence of the discrete solutions tends to the exact solution within the energy norm.