Pointwise Error Estimates for a Streamline Diiusion Scheme on a Shishkin Mesh for a Convection-diiusion Problem
نویسندگان
چکیده
We analyse a streamline diiusion scheme on a special piecewise uniform mesh for a model time-dependent convection-diiusion problem. The method with piecewise linear elements is shown to be convergent, independently of the diiusion parameter, with a pointwise accuracy of almost order 5=4 outside the boundary layer and almost order 3=4 inside the boundary layer. Numerical results are also given.
منابع مشابه
Superconvergent Approximation of Singularly Perturbed Problems
In this work, superconvergent approximation of singularly perturbed two-point boundary value problems of reaction-diiusion type and convection-diiusion type are studied. By applying the standard nite element method on the Shishkin mesh, superconvergent error bounds of (N ?1 ln(N +1)) p+1 in a discrete energy norm are established. The error bounds are uniformly valid with respect to the singular...
متن کاملGlobal and Localised A Posteriori Error Analysis in the maximum norm for finite element approx- imations of a convection-diffusion problem
We analyse nite element approximations of a stationary convection-diiusion problem. We prove global and localised a posteriori error estimates in the maximum norm. For the discretisation we use the Streamline Diiusion method.
متن کاملUniformly Convergent Nite Element Methods for Singularly Perturbed Elliptic Boundary Value Problems: Convection-diiusion Type
In this paper we consider the standard bilinear nite element method (FEM) and the corresponding streamline diiusion FEM for the singularly perturbed elliptic boundary value problem ?" (@ 2 u @x 2 + @ 2 u @y 2) ? b(x; y) ru + a (x; y)u = f (x; y) in the two space dimensions. By using the asymptotic expansion method of Vishik and Lyusternik 42] and the technique we used in 25, 26], we prove that ...
متن کاملError Estimates of a Combined Finite Volume { Finite Element Method for Nonlinear Convection { Diiusion Problems , Mm Aria Lukk a Covv A{medvid'ovv A
The subject of the paper is the analysis of error estimates of the combined nite volume-nite element method for the numerical solution of a scalar nonlinear conservation law equation with a diiusion term. Nonlinear convective terms are approximated with the aid of a monotone nite volume scheme considered over the nite volume mesh dual to a triangular grid, whereas the diiusion term is discretiz...
متن کاملNumerische Simulation Auf Massiv Parallelen Rechnern Anisotropic Mesh Reenement for Singularly Perturbed Reaction Diiusion Problems
The paper is concerned with the nite element resolution of layers appearing in singularly perturbed problems. A special anisotropic grid of Shishkin type is constructed for reaction diiusion problems. Estimates of the nite element error in the energy norm are derived for two methods, namely the standard Galerkin method and a stabilized Galerkin method. The estimates are uniformly valid with res...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995