The hp finite element method for singularly perturbed systems of reaction-diffusion equations
Date
2008ISSN
1061-5369Source
Neural, Parallel and Scientific ComputationsVolume
16Issue
3Pages
337-352Google Scholar check
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We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We present results on a high order hp finite element scheme which includes elements of size O(εp) and 0(μp) near the boundary, where ε, μ are the singular perturbation parameters and p is the degree of the approximating polynomials. Under the assumption of analytic input data, the method yields exponential rates of convergence as p → ∞, independently of ε and μ. Numerical computations supporting the theory are also presented. © Dynamic Publishers, Inc.