A priori mesh quality estimation via direct relation between truncation error and mesh distortion

DOI10.1016/j.jcp.2008.10.023zbMath1158.65015OpenAlexW2011887736MaRDI QIDQ1000948

C. Kontzialis, Yannis Kallinderis

Publication date: 12 February 2009

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2008.10.023

zbMATH Keywords

finite volume methodnumerical examplestruncation errorhybrid meshgrid distortiongrid qualityfield simulationsfirst order spatial derivativesmesh quality indicators

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical differentiation (65D25)

Related Items

High order discontinuous Galerkin discretizations with a new limiting approach and positivity preservation for strong moving shocks, Quasi-\textit{a priori} truncation error estimation and higher-order extrapolation for non-linear partial differential equations, A priori mesh quality metrics for three-dimensional hybrid grids, Linearity preserving modified LDA methods for unsteady advection-diffusion problems, Non-iterative generation of an optimal mesh for a blade passage using deep reinforcement learning, Application of discontinuous Galerkin method in supersonic and hypersonic gas flows, The estimation of truncation error by \(\tau \)-estimation revisited, A priori mesh quality metric error analysis applied to a high-order finite element method, A limiting approach for DG discretizations on mixed type meshes, On the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations

Uses Software

• Matlab
• Symbolic Math Toolbox

Cites Work

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• Triangular and quadrilateral surface mesh quality optimization using local parametrization
• Accuracy of schemes with nonuniform meshes for compressible fluid flows
• An adaptive multigrid technique for the incompressible Navier-Stokes equations
• Local adaptive mesh refinement for shock hydrodynamics
• Numerical treatment of grid interfaces for viscous flows
• A new adaptive algorithm for turbulent flows
• Truncation error analysis of the finite volume method for a model steady convective equation
• r-refinement grid adaptation algorithms and issues
• Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• Algebraic mesh quality metrics for unstructured initial meshes.
• Element residual error estimate for the finite volume method
• A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems.
• Mesh stretch effects on convection in flow simulations
• A posteriori error estimation and error control for finite element approximations of the time-dependent Navier--Stokes equations
• Analysis of stability and accuracy of finite-difference schemes on a skewed mesh
• An analysis of simplex shape measures for anisotropic meshes
• Adaptive modification of time evolving meshes