Continuously deforming finite elements.

*(English)*Zbl 0588.76147(From the summary.) The authors have introduced a general class of time- dependent co-ordinate transformations in a variational formulation for evolution problems. The variational problem is posed with respect to both solution and transformation field variables. An approximate analysis using finite elements is developed from the continuous variational form. Modified forms of the variational functional are considered to ensure the deforming mesh is not too irregular. ODE system integrators are utilized to integrate the resulting semidiscrete systems. In Part I the authors consider the formulation for problems in one spatial dimension and time, including, in particular, convection-dominated flows described by convection-diffusion, Burger’s and Buckley-Leverett equations. In part II the method is extended to two dimensions. Also presented are supporting numerical experiments.

Reviewer: P.Narain

##### MSC:

76Rxx | Diffusion and convection |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

##### Keywords:

Burger equation; meshdeforming; time-dependent co-ordinate transformations; variational formulation; evolution problems; transformation field variables; approximate analysis; continuous variational form; variational functional; ODE system integrators; semidiscrete systems; convection-dominated flows; convection-diffusion; Buckley-Leverett equations
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\textit{A. C. Mueller} and \textit{G. F. Carey}, Int. J. Numer. Methods Eng. 21, 2099--2126 (1985; Zbl 0588.76147)

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##### References:

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