Convergence of the Hundsdorfer-Verwer scheme for two-dimensional convection-diffusion equations with mixed derivative termConvergence of the Hundsdorfer-Verwer scheme for two-dimensional convection-diffusion equations with mixed derivative term
Faculty of Sciences. Mathematics and Computer Science

Applied mathematics and numerical analysis

conferenceObject

2015Melville :Amer inst physics, 2015

Mathematics

Physics

APPLIED MATHEMATICS 2014 (ICNAAM-2014)

AIP conference proceedings / American Institute of Physics. - New York

International Conference on Numerical Analysis and Applied Mathematics, (ICNAAM), SEP 22-28, 2014, Rhodes, GREECE

1648(2015), 5 p.

0094-243X

978-0-7354-1287-3

000355339705106

E

English (eng)

University of Antwerp

Alternating Direction Implicit (ADI) schemes are popular in the numerical solution of multidimensional time-dependent partial differential equations (PDEs) arising in various contemporary application fields such as financial mathematics. The Hundsdorfer-Verwer (HV) scheme is an often used ADI scheme. A structural analysis of its fundamental properties, notably convergence, is of main interest. Up to now, however, a convergence result is only known in the literature relevant to the case of one-dimensional PDEs. In this paper we prove that, under natural stability and smoothness conditions, the HV scheme has a temporal order of convergence equal to two, uniformly in the spatial mesh width, whenever it is applied to two-dimensional convection-diffusion equations with mixed derivative term.

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https://repository.uantwerpen.be/docman/irua/e11e16/126447.pdf