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Adaptivity with moving grids

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126 C. J. Budd, W. Huang and R. D. Russell<br />

W. Huang (2005b), ‘Metric tensors for anisotropic mesh generation’, J. Comput.<br />

Phys. 204, 663–665.<br />

W. Huang (2005c), ‘Convergence analysis of finite element solution of onedimensional<br />

singularly perturbed differential equations on equidistributing<br />

meshes’, Internat. J. Numer. Anal. Model. 2, 57–74.<br />

W. Huang (2007), Anisotropic mesh adaption and movement, in Adaptive Computations:<br />

Theory and Algorithms (T. Tang and J. Xu, eds), Science Press,<br />

Beijing, pp. 68–158.<br />

W. Huang and B. Leimkuhler (1997), ‘The adaptive Verlet method’, SIAM J. Sci.<br />

Comput. 18, 239–256.<br />

W. Huang and X. P. Li (2009), ‘An anisotropic mesh adaptation method for the<br />

finite element solution of variational problems’, Finite Elements in Analysis<br />

and Design, to appear.<br />

W. Huang and R. D. Russell (1996), ‘A <strong>moving</strong> collocation method for solving time<br />

dependent partial differential equations’, Appl. Numer. Math. 20, 101–116.<br />

W. Huang and R. D. Russell (1997a), ‘Analysis of <strong>moving</strong> mesh partial differential<br />

equations <strong>with</strong> spatial smoothing’, SIAM J. Numer. Anal. 34, 1106–1126.<br />

W. Huang and R. D. Russell (1997b), ‘A high dimensional <strong>moving</strong> mesh strategy’,<br />

Appl. Numer. Math. 26, 63–76.<br />

W. Huang and R. D. Russell (1999), ‘A <strong>moving</strong> mesh strategy based on a gradient<br />

flow equation for two-dimensional problems’, SIAM J. Sci. Comput. 20, 998–<br />

1015.<br />

W. Huang and R. D. Russell (2001) ‘Adaptive mesh movement: The MMPDE<br />

approach and its applications’, J. Comput. Appl. Math. 128, 383–398.<br />

W. Huang and D. Sloan (1994), ‘A simple adaptive grid method in two dimensions’,<br />

SIAM J. Sci. Comput. 15, 776–797.<br />

W. Huang and W. Sun (2003), ‘Variational mesh adaption II: Error estimates and<br />

monitor functions’, J. Comput. Phys. 184, 619–648.<br />

W. Huang and X. Zhan (2004), Adaptive <strong>moving</strong> mesh modeling for two dimensional<br />

groundwater flow and transport, in Recent Advances in Adaptive Computation,<br />

Vol. 383 of Contemporary Mathematics, AMS, pp. 283–296.<br />

W. Huang, Y. Ren, and R. D. Russell (1994), ‘Moving mesh partial differential<br />

equations (MMPDEs) based on the equidistribution principle’, SIAM J. Numer.<br />

Anal. 31, 709–730.<br />

W. Huang, L. Zheng and X. Zhan (2002), ‘Adaptive <strong>moving</strong> mesh methods for<br />

simulating one-dimensional groundwater problems <strong>with</strong> sharp <strong>moving</strong> fronts’,<br />

Internat. J. Numer. Meth. Engng 54, 1579–1603.<br />

W. Huang, J. Ma and R. D. Russell (2008), ‘A study of <strong>moving</strong> mesh PDE methods<br />

for numerical simulation of blowup in reaction diffusion equations’, J. Comput.<br />

Phys. 227, 6532–6552.<br />

W. Huang, L. Kamenski and J. Lang (2009), Anisotropic mesh adaptation based<br />

upon a posteriori error estimates. Submitted.<br />

J. M. Hyman and B. Larrouturou (1986), Dynamic rezone methods for partial<br />

differential equations in one space dimension. Technical Report LA-UR-86-<br />

1678, Los Alamos National laboratory, Los Alamos, NM.<br />

J. M. Hyman and B. Larrouturou (1989), ‘Dynamic rezone methods for partial

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