Adaptivity with moving grids

Adaptivity with moving grids 125
V. A. Dorodnitsyn (1991), ‘Transformation groups in mesh spaces’, J. Sov. Math.
55, 1490–1517.
V. A. Dorodnitsyn (1993a), Finite-difference models exactly inheriting symmetry
of original differential equations, in Modern Group Analysis: Advanced Analytical
and Computational Methods in Mathematical Physics (N. Ibragimov
et al., eds), Kluwer, Dordrecht, pp. 191–201.
V. A. Dorodnitsyn (1993b), ‘Finite difference analog of the Noether theorem’, Dokl.
Akad. Nauk 328, 678–690.
V. A. Dorodnitsyn and R. Kozlov (1997), The whole set of symmetry preserving
discrete versions of a heat transfer equation with a source. Preprint 4/1997,
NTNU, Trondheim.
A. S. Dvinsky (1991), ‘Adaptive grid generation from harmonic maps on Riemannian
manifolds’, J. Comput. Phys. 95, 450–476.
P. R. Eisman (1985), ‘Grid generation for fluid mechanics computation’, Ann. Rev.
Fluid Mech. 17, 487–522.
P. R. Eisman (1987), ‘Adaptive grid generation’, Comput. Meth. Appl. Mech. Engrg
64, 321–376.
L. C. Evans (1999), Partial differential equations and Monge–Kantorovich mass
transfer, in Current Developments in Mathematics, 1997 (Cambridge, MA),
International Press, Boston, MA, pp. 65–126.
X. Feng and M. Neilan (2009), ‘Vanishing moment method and moment solutions
for fully nonlinear second order partial differential equations’, J. Sci. Comput.,
to appear.
W. M. Feng, P. Yu, S. Y. Hu, Z. K. Liu, Q. Du and L. Q. Chen (2006), ‘Spectral implementation
of an adaptive moving mesh method for phase-field equations’,
J. Comput. Phys. 220, 498–510.
S. Fulton (1989), ‘Multigrid solution of the semigeostrophic invertibility relation’,
Monthly Weather Review 117, 2059–2066.
W. Gangbo and R. J. McCann (1996), ‘The geometry of optimal transport’, Acta
Math. 177, 113–161.
C. E. Gutiérrez (2001), The Monge–Ampère Equation, Vol. 44 of Progress in Nonlinear
Differential Equations and their Applications, Birkhäuser, Boston, MA.
S. Haker and A. Tannenbaum (2003), On the Monge–Kantorovich problem and
image warping, in Mathematical Methods in Computer Vision, Vol. 133 of
IMA Vol. Math. Appl., Springer, New York, pp. 65–85.
D. F. Hawken, J. J. Gottlieb and J. S. Hansen (1991), ‘Review of some adaptive
node-movement techniques in finite element and finite difference solutions of
PDEs’, J. Comput. Phys. 95, 254–302.
Y. He and W. Huang (2009), A posteriori error analysis for finite element solution
of elliptic differential equations using equidistributing meshes. Submitted.
W. Huang (2001a), ‘Practical aspects of formulation and solution of moving mesh
partial differential equations’, J. Comput. Phys. 171, 753–775.
W. Huang (2001b), ‘Variational mesh adaption: Isotropy and equidistribution’,
J. Comput. Phys. 174, 903–924.
W. Huang (2005a), ‘Measuring mesh qualities and application to variational mesh
adaption’, SIAM J. Sci. Comput. 26, 1643–1666.