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Adaptive refinement for convection-diffusion problems based on a defect-correction technique and finite difference method
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DOI：10.1007/BF02684469.png)
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Abstract
En 中文
A difference method is presented for singularly perturbed convection-diffusion problems with discretization error estimates of high order (order p), which hold uniformly in the singular perturbation parameter epsilon. The method is based on the use of a defect-correction technique and special adaptively graded and patched meshes, with meshsizes varying between h and epsilon(3/2)h when p = 2 where h is the meshsize, used in the part of the domain where the solution is smooth, and epsilon(3/2)h is the final meshsize in the boundary layer. Similar constructions hold for interior layers. The correction operator is a monotone operator, enabling the estimate of the error of optimal order in maximum norm. The total number of meshpoints used in a d-dimensional problem is O(epsilon(-s))h(-d) + O(h(-d)), where s is 1/p or 1/2p, respectively in the case of boundary or interior layer.
Keywords:
singularly perturbed convection-diffusion problem
defect-correction technique
finite differences
order of discretization error
adaptive refinement strategies