Domain Decomposition and Tensor Product Approximation In Adaptive Wavelet Algorithm For Second Order Elliptic BVPs

A domain decomposition (DD) technique is used to construct a piecewise tensor product wavelet basis by a univariate extension operator that, when normalised w.r.t. the energy-norm, has bounded Riesz constants. An adaptive wavelet Galerkin method is applied to solve the boundary value problem with the best nonlinear approximation rate from the basis, in linear computational complexity. Numerical experiments obtained by the adaptive wavelet Galerkin method are presented for solving elliptic problems on 2 and 3 dimensional polytopes.