A posteriori error estimate of the DSD method for first-order hyperbolic equations
type: Item
instance of: scholarly article
title: A posteriori error estimate of the DSD method for first-order hyperbolic equations
zbMATH Open document ID: 1019.65071
DOI: 10.1007/BF02437658
author: Tong Kang
author: Dehao Yu
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2003-09-08T00:00:00Z
review text: The authors establish a posteriori error estimate based on the discontinuous-streamline diffusion (DSD) method for first order hyperbolic equations. The hyperbolic equation has the form: \[ \left\{\begin{matrix} \beta\nabla u+u &=& f(x),\quad x\in\Omega,\\ u(x) &=& g(x),\quad x\in\Gamma_{-}, \end{matrix}\right. \] where \(\Omega\subset\mathbb R^2\) is a bounded domain with polygonal boundary \(\Gamma\), \(\beta=(\beta_1,\beta_2)\) are the given constants, \(\Gamma=\Gamma_{-}\cup\Gamma_{+}:\) \(\Gamma_{-}=\{x\in\Gamma:\beta\cdot n(x)<0\}\), \(n(x)\) is a unit exterior vector of \(\Gamma\) at \(x\), \(\Gamma_+=\{x\in\Gamma:\beta\cdot n(x)\geq 0\}=\Gamma/\Gamma_{-}\), the inflow boundary and the outflow boundary, respectively. A numerical example is given to illustrate the accuracy of this method.
reviewed by: Nicolae Pop
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L50
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 1880786
zbMATH Keywords: posteriori error estimate
zbMATH Keywords: discontinuous-streamline diffusion method
zbMATH Keywords: first-order hyperbolic equation
zbMATH Keywords: numerical example
MaRDI profile type: Publication
cites work: Q4241068
cites work: A posteriori error estimate of a finite-different streamline-diffusion method for a time-dependent convection-dominated diffusion equation and an adjustment technique for space mesh.
cites work: Asymptotically exact a posteriori error estimator for biquadratic elements
cites work: Q3571941
description: scientific article; zbMATH DE number 1880786