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 mu...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 L^(2)norm and first order convergence in the energy norm on graded meshes,which is independent ofε.In contrast with the conventional methods,our method is much more accurate and effective.展开更多
基金National Natural Science Foundation of China(Grant No.11301462)University Science Research Project of Jiangsu Province(Grant No.13KJB110030)Yangzhou University Overseas Study Program and New Century Talent Project to Shan Jiang。
文摘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 L^(2)norm and first order convergence in the energy norm on graded meshes,which is independent ofε.In contrast with the conventional methods,our method is much more accurate and effective.
