TY - JOUR T1 - Multiscale Basis Functions for Singular Perturbation on Adaptively Graded Meshes AU - Sun , Mei-Ling AU - Jiang , Shan JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 604 EP - 614 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m488 UR - https://global-sci.org/intro/article_detail/aamm/38.html KW - Multiscale basis functions, singular perturbation, boundary layer, adaptively graded meshes. AB -

We apply the multiscale basis functions for the singularly perturbed reaction-diffusion problem on adaptively graded meshes, which can provide a good balance between the numerical accuracy and computational cost. The multiscale space is built through standard finite element basis functions enriched with multiscale basis functions. The multiscale basis functions have abilities to capture originally perturbed information in the local problem, as a result, our method is capable of reducing the boundary layer errors remarkably on graded meshes, where the layer-adapted meshes are generated by a given parameter. Through numerical experiments we demonstrate that the multiscale method can acquire second order convergence in the L2 norm and first order convergence in the energy norm on graded meshes, which is independent of ε. In contrast with the conventional methods, our method is much more accurate and effective.