A characteristic mixed method with dynamic finite-element space for convection-dominated diffusion problems
type: Item
instance of: scholarly article
title: A characteristic mixed method with dynamic finite-element space for convection-dominated diffusion problems
zbMATH Open document ID: 0771.65065
DOI: 10.1016/0377-0427(92)90020-X
author: Daoqi Yang
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-18T00:00:00Z
review text: The method of characteristics is combined with the dynamic mixed finite element method to solve the model problem \(c(x)\partial u/\partial t+\sum^ 2_{i=1}b_ i(x)\partial u/\partial x_ i-\nabla_ 0(d(x)\nabla u)=f(x,t)\), \((x,t)\in\Omega\times J\), \(u(x,t)=0\), \((x,t)\in\Gamma\times J\), \(u(x,0)=g(x)\), \(x\in\Omega\), where \(\Omega\) is a polygonal domain in \(\mathbb{R}^ 2\) with boundary \(\Gamma\) and \(J=[0,T]\). Discretization of the transport terms along the characteristic direction is used and the mixed method for approximation of the solution and its gradient is applied. Different grids and different basis functions are implemented at different time levels in order to accurately resolve time- changing critical features. Convergence analysis and error estimates are established and some comments on the efficiency and capability of the method are made, as well.
reviewed by: K.Zlateva
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 85940
zbMATH Keywords: fronts
zbMATH Keywords: shocks
zbMATH Keywords: boundary layers
zbMATH Keywords: convection diffusion problems
zbMATH Keywords: convergence
zbMATH Keywords: method of characteristics
zbMATH Keywords: dynamic mixed finite element method
zbMATH Keywords: error estimates
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 85940