Adaptation based on interpolation errors for high order mesh refinement methods applied to conservation laws

DOI10.1016/j.apnum.2011.09.008zbMath1241.65080OpenAlexW2069443429MaRDI QIDQ412299

Pep Mulet, Antonio Baeza, Anna Martínez-Gavara

Publication date: 4 May 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.09.008

zbMATH Keywords

numerical examplesadaptive mesh refinementsemidiscretizationinterpolation errorshyperbolic conservations lawsmultiresolution algorithms

Mathematics Subject Classification ID

Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (8)

A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement ⋮ Numerical assessments of high-order accurate shock capturing schemes: Kelvin-Helmholtz type vortical structures in high-resolutions ⋮ Well-balanced adaptive mesh refinement for shallow water flows ⋮ High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes ⋮ Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws ⋮ A new family of means: the generalized weighted power means and applications ⋮ An adaptive local grid refinement method for 2D diffusion equation with variable coefficients based on block-centered finite differences ⋮ Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation

Uses Software

• RAM

Cites Work

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• Adaptive mesh refinement for conservative systems: multi-dimensional efficiency evaluation
• The piecewise parabolic method (PPM) for gas-dynamical simulations
• Adaptive mesh refinement for hyperbolic partial differential equations
• Fully adaptive multiscale schemes for conservation laws employing locally varying time stepping
• Adaptive multiresolution schemes with local time stepping for two-dimensional degenerate reaction-diffusion systems
• Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Local adaptive mesh refinement for shock hydrodynamics
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• Weighted essentially non-oscillatory schemes
• Adaptive multiresolution schemes for shock computations
• Understanding the Shu--Osher conservative finite difference form
• An adaptive version of the immersed boundary method
• A solution-adaptive upwind scheme for ideal magnetohydrodynamics
• A flux-split algorithm applied to conservative models for multicomponent compressible flows.
• An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
• Capturing shock reflections: An improved flux formula
• Efficient implementation of weighted ENO schemes
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
• Point Value Multiscale Algorithms for 2D Compressible Flows
• On the stability of fully adaptive multiscale schemes for conservation laws using approximate flux and source reconstruction strategies
• Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations
• Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations
• Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics
• Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
• On the dynamics of a shock–bubble interaction
• Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
• Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
• Fully adaptive multiresolution finite volume schemes for conservation laws
• Multiresolution algorithms for the numerical solution of hyperbolic conservation laws
• Weak solutions of nonlinear hyperbolic equations and their numerical computation
• Multiresolution schemes for conservation laws

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