Abstract
The accurate and efficient discretization of singularly perturbed advection-diffusion equations on arbitrary domains remains an open problem. An interesting approach to tackle this problem is the complete flux scheme (CFS) proposed by G.D. Thiart and further investigated by J. ten Thije Boonkkamp. For the CFS, uniform second order convergence has been proven on structured grids. We extend a version of the CFS to nonuniform grids, predict an error bound and numerically verify it for a solution to an ODE with a boundary layer.
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Farrell, P., Linke, A. (2017). Uniform Second Order Convergence of a Complete Flux Scheme on Nonuniform 1D Grids. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_23
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DOI: https://doi.org/10.1007/978-3-319-57397-7_23
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