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Adaptive Moving Mesh Methods
Preface.- Introduction.- Adaptive Mesh Movement in 1D.- Discretization of PDEs on Time-Varying Meshes.- Basic Principles of Multidimensional Mesh Adaption.- Monitor Functions.- Variational Mesh
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
This paper considers several moving mesh partial differential equations that are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh
Adaptivity with moving grids
In this article we survey r-adaptive (or moving grid) methods for solving time-dependent partial differential equations (PDEs). Although these methods have received much less attention than their h-
Analysis Of Moving Mesh Partial Differential Equations With Spatial Smoothing
Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh
Moving Mesh Methods for Problems with Blow-Up
This paper considers moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs), and it is shown that for suitable ones the MMPDE solution evolves towards a (moving) mesh which close to the blow-up point automatically places the mesh points in such a manner that the ignition kernel approaches a constant as $t\to T$ (theblow-up time).
Pole condition for singular problems: the pseudospectral approximation
Abstract This paper deals with the pseudospectral solution of differential equations with coordinate singularities such as those which describe situations in spherical or cylindrical geometries. We
Metric tensors for anisotropic mesh generation
It has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of
Moving Mesh Methods Based on Moving Mesh Partial Differential Equations
Several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh PDEs derived in a previous paper. These versions are quite simple and easy to
Practical aspects of formulation and solution of moving mesh partial differential equations
Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are
A Moving Mesh Method Based on the Geometric Conservation Law
A new adaptive mesh movement strategy is presented, which, unlike many existing moving mesh methods, targets the mesh velocities rather than the mesh coordinates, and bears a close relation with the Lagrangian method.