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A symmetric characteristic finite volume element scheme for nonlinear convection-diffusion problems

A symmetric characteristic finite volume element scheme for nonlinear convection-diffusion problems In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H 1-norm error estimates of order O(Δt 2 + h) and present some numerical examples at the end of the paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A symmetric characteristic finite volume element scheme for nonlinear convection-diffusion problems

Acta Mathematicae Applicatae Sinica , Volume 24 (1) – Mar 13, 2008

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-005-5183-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems. Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H 1-norm error estimates of order O(Δt 2 + h) and present some numerical examples at the end of the paper.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 13, 2008

References