Abstract
A singularly perturbed elliptic problem of reaction-diffusion type is examined. The solution is decomposed into a sum of a regular component, boundary layer components and corner layer components. Numerical approximations are generated separately for each of these components. These approximations are patched together to form a global approximation to the solution of the continuous problem. An asymptotic error bound in the pointwise maximum norm is established; whose dependence on the values of the singular perturbation parameter is explicitly identified. Numerical results are presented to illustrate the performance of the numerical method.
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Falco, C.d., O’Riordan, E. (2009). A Patched Mesh Method for Singularly Perturbed Eeaction-Diffusion Equations. In: Hegarty, A., Kopteva, N., O'Riordan, E., Stynes, M. (eds) BAIL 2008 - Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00605-0_8
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DOI: https://doi.org/10.1007/978-3-642-00605-0_8
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