Global uniformly convergent schemes for a singularly perturbed boundary-value problem using patched base spline-functions

Global Uniformly Convergent Nite Element Methods for Singularly Perturbed Elliptic Boundary Value Problems: Higher-order Elements

{ In this paper, we develop a general higher-order nite element method for solving singularly perturbed elliptic linear and quasilinear problems in two space dimensions. We prove that a quasioptimal global uniform convergence rate of O(N ?(m+1) x ln m+1 N x + N ?(m+1) y ln m+1 N y) in L 2 norm is obtained for a reaction-diiusion model by using the m-th order (m 2) tensor-product element, thus a...

A Global Uniformly Convergent Finite Element Method for a Quasilinear Singularly Perturbed Elliptic Problem

Uniformly 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 ...

Uniformly Convergent Finite Element Methods for Singularly Perturbed Elliptic Boundary Value Problems I: Reaction-diffusion Type

{ We consider the bilinear nite element method on a Shishkin mesh for the singularly perturbed elliptic boundary value problem ?" 2 (@ 2 u @x 2 + @ 2 u @y 2) + a(x; y)u = f(x; y) in two space dimensions. By using a very sophisticated asymptotic expansion of Han et al. 11] and the technique we used in 17], we prove that our method achieves almost second-order uniform convergence rate in L 2-norm...

Solution of a Fourth Order Singularly Perturbed Boundary Value Problem Using Quintic Spline

Singularly perturbed boundary value problem can be solved using various techniques. The solution of the following fourth order self adjoint singularly perturbed boundary value problem is approximated using quintic spline Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(1)(a) = α2, y(1)(b) = α3, } or Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(2)(a) = α4, y...