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The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes.
Calculus of variations
I. M. Gelfand and S. V. Fomin · 1963
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Adaptive mesh zoning by the equipotential method
A. M. Winslow · 1981
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Adaptive zoning for singular problems in two dimensions
J. U. Brackbill and J. S. Saltzman · 1982
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Numerical grid generation
J. F. Thompson, Z. U. A. Warsi, and C. W. Mastin · 1985
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On the convergence of iterated remeshing
J. D. Pryce · 1989
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Adaptive grid generation from harmonic maps on Riemannian manifolds
A. S. Dvinsky · 1991
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Moving mesh methods based on moving mesh partial differential equations
W. Huang, Y. Ren, and R. D. Russell · 1994
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Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
W. Huang, Y. Ren, and R. D. Russell · 1994
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Fundamentals of grid generation
P. M. Knupp and S. Steinberg · 1994
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On diagonal dominance of stiffness matrices in 3 3 D
M. Křížek and Q. Lin · 1995
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Jacobian-weighted elliptic grid generation
P. M. Knupp · 1996
Earlier work this paper cites.
Dynamical systems and numerical analysis , volume 2 of Cambridge Monographs on Applied and Computational Mathematics
A. M. Stuart and A. R. Humphries · 1996
Cited alongside, same era.
Computational grids
G. F. Carey · 1997
Cited alongside, same era.
Tetrahedral mesh improvement using swapping and smoothing
L. A. Freitag and C. Ollivier-Gooch · 1997
Cited alongside, same era.
A high-dimensional moving mesh strategy
W. Huang and R. D. Russell · 1998
Cited alongside, same era.
Moving mesh strategy based on a gradient flow equation for two-dimensional problems
W. Huang and R. D. Russell · 1999
Cited alongside, same era.
Grid generation methods
V. D. Liseikin · 1999
Cited alongside, same era.
Metric tensors for anisotropic mesh generation
W. Huang · 2005
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Adaptive Moving Mesh Methods , volume 174 of Applied Mathematical Sciences
W. Huang and R. D. Russell · 2011
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Convergence of de Boor’s algorithm for the generation of equidistributing meshes
X. Xu, W. Huang, R. D. Russell, and J. F. Williams · 2011
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Domain decomposition approaches for mesh generation via the equidistribution principle
M. J. Gander and R. D. Haynes · 2012
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Energy-diminishing integration of gradient systems
E. Hairer and C. Lubich · 2014
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Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems
C. Lu, W. Huang, and J. Qiu · 2014
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A framework for variational grid generation: conditioning the Jacobian matrix with matrix norms
P. M. Knupp and N. Robidoux · 2000
Cited alongside, same era.
A moving mesh finite element method for the solution of two-dimensional Stefan problems
G. Beckett, J. A. Mackenzie, and M. L. Robertson · 2001
Cited alongside, same era.
Variational mesh adaptation: isotropy and equidistribution
W. Huang · 2001
Cited alongside, same era.
Moving mesh methods in multiple dimensions based on harmonic maps
R. Li, T. Tang, and P. Zhang · 2001
Cited alongside, same era.
Variational mesh adaptation. II. Error estimates and monitor functions
W. Huang and W. Sun · 2003
Cited alongside, same era.
Anisotropic mesh quality measures and adaptation for polygonal meshes
W. Huang and Y. Wang
Cited in the paper.
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A geometric discretization and a simple implementation for variational mesh generation and adaptation
W. Huang and L. Kamenski · 2015
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Mesh smoothing: an MMPDE approach, 2015
W. Huang, L. Kamenski, and H. Si · 2015
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TetGen, a Delaunay-based quality tetrahedral mesh generator
H. Si · 2015
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Tetrahedral mesh improvement using moving mesh smoothing and lazy searching flips
F. Dassi, L. Kamenski, and H. Si · 2016
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Discrete analysis of domain decomposition approaches for mesh generation via the equidistribution principle
R. D. Haynes and F. Kwok · 2017
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