Adaptive boundary element methods with convergence rates
It provides theoretical foundations for adaptive boundary element methods, analogous to adaptive finite element methods, benefiting computational mathematics and engineering applications.
This paper develops adaptive boundary element methods for operator equations of positive, negative, and zero order, proving quasi-optimal convergence rates under mild assumptions without saturation-type assumptions.
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense under mild assumptions that are analogous to what is typically assumed in the theory of adaptive finite element methods. In particular, no saturation-type assumption is used. The main ingredients of the proof that constitute new findings are some results on a posteriori error estimates for boundary element methods, and an inverse-type inequality involving boundary integral operators on locally refined finite element spaces.