Numerical solution of multidimensional hyperbolic PDEs using defect correction on adaptive grids
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Publication:2014027
DOI10.1007/s10915-016-0209-6zbMath1372.65243OpenAlexW2336524022MaRDI QIDQ2014027
M. Razi, Prakash Vedula, Peter J. Attar
Publication date: 10 August 2017
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-016-0209-6
numerical exampleBurgers equationLiouville equationlocal truncation errordimensional splittingorder of accuracynonlinear hyperbolic equationnon-iterative defect correctionadaptive finite difference solutionmodified differential equationmultidimensional hyperbolic equations
KdV equations (Korteweg-de Vries equations) (35Q53) Second-order nonlinear hyperbolic equations (35L70) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Uses Software
Cites Work
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- Boosting the accuracy of finite difference schemes via optimal time step selection and non-iterative defect correction
- A critical analysis of the modified equation technique of warming and Hyett
- Grid adaptation and non-iterative defect correction for improved accuracy of numerical solutions of PDEs
- The piecewise parabolic method (PPM) for gas-dynamical simulations
- Adaptive mesh refinement for hyperbolic partial differential equations
- Numerical experiments on the accuracy of ENO and modified ENO schemes
- A numerical study of the convergence properties of ENO schemes
- Error estimates for deferred correction methods in time
- Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs
- Full Eulerian simulations of biconcave neo-Hookean particles in a Poiseuille flow
- Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
- High resolution schemes for hyperbolic conservation laws
- Adaptive grid generation
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
- A stable and accurate convective modelling procedure based on quadratic upstream interpolation
- The method of fractional steps for conservation laws
- Application of a second-order Godunov-type finite difference scheme to a nonlinear elastodynamic problem
- The modified equation approach to the stability and accuracy analysis of finite-difference methods
- Piecewise monotone interpolation
- On the method of modified equations. I: Asymptotic analysis of the Euler forward difference method
- Weighted essentially non-oscillatory schemes
- One-dimensional adaptive grid generation
- A split step approach for the 3-D Maxwell's equations
- Deferred correction in space and time
- Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
- Efficient implementation of weighted ENO schemes
- High-order remapping with piece-wise parabolic reconstruction
- Efficient implementation of high order unstructured WENO schemes for cavitating flows
- A bounded upwinding scheme for computing convection-dominated transport problems
- Heuristic stability theory for finite-difference equations
- A new method for solving two-point boundary value problems using optimal node distribution
- A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
- Extension of high-order compact schemes to time-dependent problems
- Modified Essentially Nonoscillatory Schemes Based on Exponential Polynomial Interpolation for Hyperbolic Conservation Laws
- Grid adaption for problems in fluid dynamics
- Accurate Monotonicity Preserving Cubic Interpolation
- Splitting methods
- Nonnegativity-, Monotonicity-, or Convexity-Preserving Cubic and Quintic Hermite Interpolation
- Well-balanced compressible cut-cell simulation of atmospheric flow
- Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- Nonlinear truncation error analysis of finite difference schemes forthe Euler equations
- Grading Functions and Mesh Redistribution
- A Test of Moving Mesh Refinement for 2-D Scalar Hyperbolic Problems
- A Theoretical Framework for Proving Accuracy Results for Deferred Corrections
- A‐posteriori error estimates for the finite element method
- On Selection of Equidistributing Meshes for Two-Point Boundary-Value Problems
- The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
- Local Piecewise Hyperbolic Reconstruction of Numerical Fluxes for Nonlinear Scalar Conservation Laws
- Composition constants for raising the orders of unconventional schemes for ordinary differential equations
- Practical Extrapolation Methods
- A convergent and universally bounded interpolation scheme for the treatment of advection
- High‐order compact scheme for the steady stream‐function vorticity equations
- Robust Numerical Coupling of Pressure and Pressureless Gas Dynamics Equations for Eulerian Spray DNS and LES
- Two alternatives for solving hyperbolic boundary value problems of geophysical fluid dynamics
- Geometric Numerical Integration
- On the Construction and Comparison of Difference Schemes
- Minimization of the truncation error by grid adaptation
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