General formulation of second-order semi-Lagrangian methods for convection-diffusion problems
type: Item
instance of: scholarly article
title: General formulation of second-order semi-Lagrangian methods for convection-diffusion problems
zbMATH Open document ID: 1266.65156
DOI: 10.1155/2013/763630
author: Xiaohan Long
author: Chuanjun Chen
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: The general formulation of the second-order semi-Lagrangian methods is presented for convection-dominated diffusion problems. In view of the method of lines, this formulation is in a sufficiently general fashion as to include the two-step backward difference formula and Crank-Nicolson type semi-Lagrangian schemes as particular ones. It is easy to be extended to higher-order schemes. We show that it maintains second-order accuracy even if the involved numerical characteristic lines are first-order accurate. The relationship between semi-Lagrangian methods and the modified method of characteristic is also addressed. Finally, convergence properties of the semi-Lagrangian finite difference schemes are tested.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6161371
zbMATH Keywords: convection-diffusion problems
zbMATH Keywords: comparison of methods
zbMATH Keywords: second-order semi-Lagrangian methods
zbMATH Keywords: method of lines
zbMATH Keywords: backward difference formula
zbMATH Keywords: Crank-Nicolson type
zbMATH Keywords: method of characteristic
zbMATH Keywords: convergence
zbMATH Keywords: finite difference schemes
Wikidata QID: Q58917404
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/763630
OpenAlex ID: W1990065092
cites work: On the solution of nonlinear hyperbolic differential equations by finite differences
cites work: Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
cites work: Characteristic-Galerkin Methods for Contaminant Transport with Nonequilibrium Adsorption Kinetics
cites work: The approximation of the pressure by a mixed method in the simulation of miscible displacement
cites work: Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
cites work: Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
cites work: A summary of numerical methods for time-dependent advection-dominated partial differential equations
cites work: On the Construction and Comparison of Difference Schemes
cites work: A second order characteristic finite element scheme for convection-diffusion problems
cites work: A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations
cites work: A high order characteristics method for the incompressible Navier-Stokes equations
cites work: A high-order characteristics/finite element method for the incompressible Navier-Stokes equations
cites work: Numerical Analysis of Convection‐Diffusion‐Reaction Problems with Higher Order Characteristics/Finite Elements. Part I: Time Discretization
cites work: Numerical Analysis of Convection‐Diffusion‐Reaction Problems with Higher Order Characteristics/Finite Elements. Part II: Fully Discretized Scheme and Quadrature Formulas
cites work: A second-order time-accurate ALE Lagrange-Galerkin method applied to wind engineering and control of bridge profiles
cites work: A semi-Lagrangian high-order method for Navier-Stokes equations
cites work: Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows
cites work: Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
cites work: Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation
cites work: Multi-dimensional conservative semi-Lagrangian method of characteristics CIP for the shallow water equations
cites work: Q3779682
cites work: Q5674335
cites work: Finite element methods for nonlinear parabolic equations
cites work: Multistep characteristic method for incompressible flow in porous media
description: scientific article; zbMATH DE number 6161371