An Adaptive Wavelet Method for Semi-Linear First-Order System Least Squares

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 $\vec{H}_{0,\Gamma _N}(\operatorname{div};\Omega )$ on general polygons. The theoretical findings are illustrated by numerical experiments.

CUBIC SPLINE ADAPTIVE WAVELET SCHEME TO SOLVE SINGULARLY PERTURBED REACTION DIFFUSION PROBLEMS

In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented for elliptic and parabolic problems. The purposed method comes up as a powerful tool for studying singular perturbation problems in term of effective grid generation and CPU time.