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Adaptivity with moving grids (Q3638929)

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Language	Label	Description	Also known as
English	Adaptivity with moving grids	scientific article

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scholarly article

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Adaptivity with moving grids (English)

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zbMATH Open document ID

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10.1017/S0962492906400015

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Robert D. Russell

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publication date

28 October 2009

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

finite difference method with moving meshs

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multigrids methods

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error estimate

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singularities

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shocks

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changes of phase

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reaction-diffusion systems

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Adaptive moving mesh methods for two-dimensional resistive magneto-hydrodynamic PDE models

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Mesh Smoothing Using A Posteriori Error Estimates

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A competitive (dual) simplex method for the assignment problem

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The nonlinear Schrödinger equation. Self-focusing and wave collapse

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Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

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A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws

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A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries

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On the finite element method

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An adaptive mesh redistribution algorithm for convection-dominated problems

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Analysis of Optimal Finite-Element Meshes in R 1

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Collocation Software for Boundary-Value ODEs

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On Legendre transformations and umbilic catastrophes

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A moving grid finite‐element method using grid deformation

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Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation

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Domain Deformation Mapping: Application to Variational Mesh Generation

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A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations

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MOVCOL4: A Moving Mesh Code for Fourth‐Order Time‐Dependent Partial Differential Equations

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An iterative grid redistribution method for singular problems in multiple dimensions

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Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence

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Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid

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Numerical solution of Fisher's equation using a moving mesh method

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On the Convergence of Iterated Remeshing

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Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations

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On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I

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Pseudospectral Solution of Near-Singular Problems using Numerical Coordinate Transformations Based on Adaptivity

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On the Volume Elements on a Manifold

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Adaptive local overlapping grid methods for parabolic systems in two space dimensions

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Moving Finite Elements. I

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Moving Finite Elements. II

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Local Piecewise Hyperbolic Reconstruction of Numerical Fluxes for Nonlinear Scalar Conservation Laws

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Symplectic integration of Hamiltonian wave equations

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A moving mesh method for the solution of the one-dimensional phase-field equations

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An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh

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Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid

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Relationship between tetrahedron shape measures

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Moving meshes by the deformation method

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On the Error of Linear Interpolation and the Orientation, Aspect Ratio, and Internal Angles of a Triangle

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Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains

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Boundary regularity of maps with convex potentials. II

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The Regularity of Mappings with a Convex Potential

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Self-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations

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Adaptive moving mesh computations for reaction--diffusion systems

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Self–similar numerical solutions of the porous–medium equation using moving mesh methods

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On resistive MHD models with adaptive moving meshes

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New self-similar solutions of the nonlinear Schrödinger equation with moving mesh computations

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Moving Mesh Methods for Problems with Blow-Up

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Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions

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Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation

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Adaptive grid generation

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Mesh generation using vector-fields

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Smooth Regrading of Discretized Data

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Equidistributing Meshes with Constraints

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Computing the Kantorovich distance for images

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Structured mesh adaption: Space accuracy and interpolation methods

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A mechanical model for a new grid generation method in computational fluid dynamics

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Dynamic rezone methods for partial differential equations in one space dimension

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Adaptive grid generation from harmonic maps on Riemannian manifolds

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Transformation groups in network spaces

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Simple adaptive grids for 1-D initial value problems

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Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations

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An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization

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Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: a least-squares approach

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Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: An augmented Lagrangian approach

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An Interpolation Error Estimate on Anisotropic Meshes in ${\mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement

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A new approach to grid generation

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Stability of Moving Mesh Systems of Partial Differential Equations

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Moving mesh methods with upwinding schemes for time-dependent PDEs

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A moving mesh finite element algorithm for singular problems in two and three space dimensions

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A moving collocation method for solving time dependent partial differential equations

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The Adaptive Verlet Method

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Measuring Mesh Qualities and Application to Variational Mesh Adaptation

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Variational mesh adaptation: Isotropy and equidistribution

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Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D

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A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem

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Reference Jacobian optimization-based rezone strategies for arbitrary Lagrangian Eulerian methods

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A Framework for Variational Grid Generation: Conditioning the Jacobian Matrix with Matrix Norms

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Algebraic Mesh Quality Metrics

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Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations

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Jacobian-Weighted Elliptic Grid Generation

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Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm

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Error Equidistribution and Mesh Adaptation

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A fully implicit, nonlinear adaptive grid strategy

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An efficient dynamically adaptive mesh for potentially singular solutions

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Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions

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Design and Application of a Gradient-Weighted Moving Finite Element Code I: in One Dimension

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Approaches for generating moving adaptive meshes: Location versus velocity

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A Moving Mesh Method Based on the Geometric Conservation Law

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A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation

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An \(r\)-adaptive finite element method based upon moving mesh PDEs

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An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

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Anisotropic Measures of Third Order Derivatives and the Quadratic Interpolation Error on Triangular Elements

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The geometry of optimal transportation

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Spectral implementation of an adaptive moving mesh method for phase-field equations

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A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations

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Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

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Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle

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Variational mesh adaptation. II: Error estimates and monitor functions

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A Simple Adaptive Grid Method in Two Dimensions

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Adaptive mesh movements -- the MMPDE approach and its applications

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Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems

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A high dimensional moving mesh strategy

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Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing

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Generalised Lagrangian Solutions for Atmospheric and Oceanic Flows

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Adaptive zoning for singular problems in two dimensions

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Analysis and computation of adaptive moving grids by deformation

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Boundary-fitted coordinate systems for numerical solution of partial differential equations. A review

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