Adaptive multiresolution mesh refinement for the solution of evolution PDEs

In this paper we propose a novel multiresolution adaptive mesh refinement algorithm for solving initial-boundary value problems (IBVP) for evolution partial differential equations. The proposed algorithm dynamically adapts the grid to any existing or emerging irregularities in the solution, thus refining the grid only at places where the solution exhibits sharp features. The main advantage of the proposed grid adaptation method is that it results in a grid with a fewer number of nodes when compared to adaptive grids generated by other wavelet- or multiresolution-based mesh refinement techniques. Several examples show the robustness, stability and savings (in terms of CPU time) of our algorithm.