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Pointwise convergence of approximations to a convection–diffusion equation on a Shishkin mesh

✍ Scribed by Wim Lenferink

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
140 KB
Volume
32
Category
Article
ISSN
0168-9274

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✦ Synopsis

A centered difference or finite element discretization is applied to a singularly perturbed, one-dimensional boundary value problem. The discretization uses a piecewise equidistant mesh. It is proved that the pointwise error is (almost) of second order with respect to the number of nodes, uniformly in the perturbation parameter. The proof is based on a monotonicity argument.

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