How accurate is the streamline diffusion finite element method?
نویسندگان
چکیده
منابع مشابه
How accurate is the streamline diffusion finite element method?
We investigate the optimal accuracy of the streamline diffusion finite element method applied to convection–dominated problems. For linear/bilinear elements the theoretical order of convergence given in the literature is either O(h3/2) for quasi–uniform meshes or O(h2) for some uniform meshes. The determination of the optimal order in general was an open problem. By studying a special type of m...
متن کاملAn Optimal Streamline Diffusion Finite Element Method for a Singularly Perturbed Problem
The stability and accuracy of a streamline diffusion finite element method (SDFEM) on arbitrary grids applied to a linear 1-d singularly perturbed problem are studied in this paper. With a special choice of the stabilization quadratic bubble function, the SDFEM is shown to have an optimal second order in the sense that ‖u − uh‖∞ ≤ C infvh∈V h ‖u − vh‖∞, where uh is the SDFEM approximation of th...
متن کاملAnalysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem
Abstract. In this paper, a bilinear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection – diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter ǫ provided only that ǫ ≤ N. An O(N(lnN)) convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumpti...
متن کاملFinite Element Methods for Convection Diffusion Equation
This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...
متن کاملAdaptive Streamline Diffusion Finite Element Methods for Stationary Convection-diffusion Problems
Adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed. A priori error estimates ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1997
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-97-00788-6