An Adaptive Wavelet Method for Semi-Linear First-Order System Least Squares
Nabi Chegini, Rob P. Stevenson · Computational Methods in Applied Mathematics · 2015
Abstract We design an adaptive wavelet scheme for solving first-order system least-squares formulations of second-order elliptic PDEs that converge with the best possible rate in linear complexity. A wavelet Riesz basis is constructed for the space H → 0 , Γ N ( div ; Ω ) $\vec{H}_{0,\Gamma _N}(\operatorname{div};\Omega )$ on general polygons. The theoretical findings are illustrated by numerical experiments.