Year: 2020
Author: Yuxia Li, Cong Xie, Xinglong Feng
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 158–180
Abstract
A novel streamline diffusion form of virtual element method for convection-dominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(x)∇$v$)−b(x)·∇$v$). Unlike the standard VEM, the stabilisation scheme can efficiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.231118.240619
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 158–180
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Convection dominated diffusion problem streamline diffusion virtual element method stabilisation optimal convergence boundary layer problem.