The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing N for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on and meshes. It is shown that the combination FEM yields (up to a factor ln N) the same order of accuracy in the associated energy norm as the Galerkin FEM on an N × N mesh, but it requires only (N ^3/2) degrees of freedom compared with the (N ²) used by the Galerkin FEM. An analogous result is also proved for the streamline diffusion finite element method. This work was supported by the National Natural Science Foundation of China (10701083 and 10425105), the Chinese National Basic Research Program (2005CB321704) and the Boole Centre for Research in Informatics at National University of Ireland Cork.     

ChemInform Abstract: Matrix Infrared Spectra and Electronic Structure Calculations of the First Actinide Borylene: FB=ThF2.

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