Uniformly Convergent Finite Element Methods for Singularly Perturbed Elliptic Boundary Value Problems I: Reaction-diffusion Type
نویسنده
چکیده
{ 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. Numerical results connrm our theoretical analysis.
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