Adaptive multiresolution approach for two-dimensional PDEs Original Research Article

A multiresolution adaptive approach for the solution of two-dimensional partial differential equations (PDEs) is presented. This methodology is a multidimensional extension of that presented in a previous work [Comput. Methods Appl. Mech. Engrg. 191 (2002) 3909]. The method proposed is unconditionally stable, by incorporating convection differencing schemes with the TVD property, and the grid is dynamically adapted so that higher spatial resolution is automatically allocated to domain regions where strong gradients are observed. The two desired properties of any PDE solver, stability and accuracy, are therefore retained. Numerical results for four test problems are presented which serve to demonstrate the robustness and cost effectiveness of the method.