An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
Computational solution of two-dimensional unsteady PDEs using moving mesh methods
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
Efficient computation of dendritic growth with r-adaptive finite element methods
Journal of Computational Physics
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The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge-Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R.Li, T.Tang, P.W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, Journal of Computational Physics, 177 (2002) 365-393]. A Beckett and Mackenzie type monitor function is adopted. To obtain high quality meshes around the wetting front, a smoothing method which is based on the diffusive mechanism is used. With the moving mesh technique, high mesh quality and high numerical accuracy are obtained successfully. The numerical convergence and the advantage of the algorithm are demonstrated by a series of numerical experiments.