Open AccessBook
Moving finite elements
TLDR
This book brings together most of the work done over the last decade or so which has been stimulated by Miller's original idea, and discusses the interrelationships between the techniques and the established ideas of the method of characteristics, Hamilton's equations, the Legendre transformation, and grid equidistribution.Abstract:
This book is mainly concerned with finite element methods for time-dependent partial differential equations when the grids are allowed to move in time, but also describes grid generation techniques which include grid adjustment. The mechanism for grid movement derives from a generalization of the residual minimization technique which is familiar from the Galerkin finite element method. The book brings together most of the work done over the last decade or so which has been stimulated by Miller's original idea, and discusses the interrelationships between the techniques of the method and the established ideas of the method of characteristics, Hamilton's equations, the Legendre transformation, and grid equidistribution. The book highlights the issues involved and should provide the reader with a clear view of the current state of the subject and prompt further research.read more
Citations
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Torsional springs for two-dimensional dynamic unstructured fluid meshes
TL;DR: In this paper, the authors proposed a method to control the arbitrary motion of two-dimensional dynamic unstructured fluid grids with additional torsional springs, which can be designed to prevent the interpenetration of neighboring triangles.
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Upscaling: a review
TL;DR: In this paper, the authors present averaging techniques, devised to simulate large scale features of solutions without necessarily solving all the fine scale equations, which can be used to solve the fluid flow equations.
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Adaptivity with moving grids
TL;DR: R-adaptive methods have enormous potential and indeed can produce an optimal form of adaptivity for many problems, including scale-invariant problems, blow-up problems, problems with moving fronts and problems in meteorology.
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A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems
TL;DR: Tarzia et al. as discussed by the authors presented a bibliografía on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems, which contains 5869 titles referring to 588 scientific journals, 122 books, 88 symposia, 30 collections, 59 thesis and 247 technical reports.
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Moving mesh methods in multiple dimensions based on harmonic maps
Ruo Li,Tao Tang,Pingwen Zhang +2 more
TL;DR: This work will extend Dvinsky's method to provide an efficient solver for the mesh-redistribution algorithm, which adapts the mesh extremely well to the solution without producing skew elements for multi-dimensional computations.
References
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Numerical study of slightly viscous flow
TL;DR: In this paper, a numerical method for solving the time-dependent Navier-Stokes equations in two space dimensions at high Reynolds number is presented, where the crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers.
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Generalized finite-difference schemes
Blair Swartz,Burton Wendroff +1 more
TL;DR: Galerkin's method, using a local basis, provides unconditionally stable, implicit generalized finite-difference schemes for a large class of linear and nonlinear problems.
A NUMERICAL and ANALYTICAL STUDY OF ANOMALOUS PROPAGATION OF ELECTRICAL IMPULSES IN DAMAGED HEART FIBERS
TL;DR: In this paper, the authors propose a solution to solve the problem of the problem: this paper...,.. ].. ).. ]... )..