Adaptive wavelet methods for elliptic operator equations with nonlinear terms
The authors present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. The method is developed based on tree approximation for the solution of the equations and an adaptive fast reconstruction of nonlinear functionals of the wavelet expansions. A constructive greedy scheme is introduced. These adaptive methods generate approximate solutions with optimal order in both convergence and computational complexity when the solutions have certain degree of Besov regularity.
scientific article; zbMATH DE number 1903991