Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems |
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Authors: | SUN GUANGFU; STYNE MARTIN |
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Institution: |
Department of Mathematics, University College Cork, Ireland
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Abstract: | e-mail address: stynes{at}bureau.ucc.ie We consider singularly perturbed high-order elliptic two-pointboundary value problems of convection-diffusion type. Undersuitable hypotheses, the coercivity of the associated bilinearform is proved and a representation result for the solutionsof such problems is given. A family of Galerkin finite-elementmethods based on piecewise polynomial test/trial functions ona Shishkin mesh is constructed and proved to be convergent,uniformly in the perturbation parameter, in energy and W norms. Numerical results are presentedfor a second-order problem and fourth-order problems. |
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Keywords: | |
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