Hans-Görg Roos, Martin Schopf (2012)
Applications of Mathematics
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So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
Roos, Hans-Görg, Zarin, Helena (2003)
Novi Sad Journal of Mathematics
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Çakır, Musa, Amiraliyev, Gabil M. (2010)
Journal of Applied Mathematics
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Vinod Kumar, Rajesh Bawa, Arvind Lal (2014)
International Journal of Applied Mathematics and Computer Science
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Vinod Kumar, Rajesh Bawa, Arvind Lal (2014)
International Journal of Applied Mathematics and Computer Science
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Eugene O’Riordan (2012)
Open Mathematics
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In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference...