A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with spec...A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded （based on a mesh generating function） in the fine mesh region. Error estimates in the s-weighted energy norm are proved. We derive an ＇optimal＇ mesh generating function in order to min- imize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving er- ror estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.展开更多
文摘A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded （based on a mesh generating function） in the fine mesh region. Error estimates in the s-weighted energy norm are proved. We derive an ＇optimal＇ mesh generating function in order to min- imize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving er- ror estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.
