Abstract
In this paper, an arbitrary order finite element method is developed on an anisotropically refined mesh for solving singular perturbation problems in two and three space dimensions. Especially, for a weak convection-diffusion problem, we prove that a quasioptimal global uniform convergence rate of in L 2 norm is obtained for the m-th (m ≥ 1) order tensor-product finite element, thus answering some open problems posed by Roos in [17]. Here Nx and Ny are the number of partitions in the x-and y-directions, respectively. Numerical results supporting our theoretical analysis are provided. Generalizations of our techniques to other singular perturbation problems are mentioned.
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