An Adaptive Method using the L-Weno Reconstruction

Abstract

In this work, an adaptive formulation of the Legendre - Weighted Essentially Non-Oscillatory (L-WENO) method is used to solve some problems of two-dimensional linear conservation laws on unstructured triangular mesh. The mesh adaptivity is used to improve the performance of the method. Although the results with the L-WENO method gets better as the mesh is refined, the mesh adaptation algorithm was able to improve the quality of the numerical approximation and reduce computational cost by refining and coarsening the computational mesh based on some specified criteria.