Quantification of errors for operator-split advection-diffusion calculations

DOI10.1016/j.cma.2014.01.005zbMath1296.65119OpenAlexW2042969001MaRDI QIDQ459087

Jeffrey W. Banks, Carol S. Woodward, Jeffrey A. F. Hittinger, Jeffrey Mark Connors

Publication date: 8 October 2014

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.01.005

zbMATH Keywords

error estimationadvection-diffusionoperator splittinga posteriori erroradjoint error

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

A comparison of boundary correction methods for Strang splitting ⋮ A Posteriori Analysis and Efficient Refinement Strategies for the Poisson--Boltzmann Equation ⋮ Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions ⋮ Comparison of efficiency among different techniques to avoid order reduction with Strang splitting ⋮ Avoiding order reduction when integrating reaction-diffusion boundary value problems with exponential splitting methods ⋮ A modified Gautschi's method without order reduction when integrating boundary value nonlinear wave problems

Uses Software

• CAM3

Cites Work

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• Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems
• A fast explicit operator splitting method for passive scalar advection
• A posteriori error analysis for a cut cell finite volume method
• A posteriorierror analysis of a cell-centered finite volume method for semilinear elliptic problems
• Efficient implementation of chemistry in computational combustion
• A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer
• Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems
• High-order splitting methods for the incompressible Navier-Stokes equations
• Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations.
• Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling
• An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow
• A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection
• Consistency of iterative operator-splitting methods: Theory and applications
• Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
• An A Posteriori–A Priori Analysis of Multiscale Operator Splitting
• Numerical Methods Based on Additive Splittings for Hyperbolic Partial Differential Equations
• Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
• Estimating the error of numerical solutions of systems of reaction-diffusion equations
• The Theoretical Accuracy of Runge–Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error
• Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
• A Posteriori Analysis and Adaptive Error Control for Multiscale Operator Decomposition Solution of Elliptic Systems I: Triangular Systems
• On the Construction and Comparison of Difference Schemes
• Difference schemes for hyperbolic equations with high order of accuracy
• Fractional step methods applied to a chemotaxis model

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