A moving finite element method for the solution of two-dimensional time-dependent models. (English) Zbl 1013.65107

Summary: A moving finite element method is developed to solve time dependent problems in two space dimensions. In this formulation the solution is approximated by a piecewise polynomial of high degree on a hexagonally connected triangular mesh. Special treatment, such as the way of calculating the integrals involving second spatial derivatives and the way of preventing singularities are introduced and discussed. Numerical experiments are employed to illustrate the relationship between the nodes movements and the choice of penalty constants as well as to test the accuracy and efficiency of the proposed method.


65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs


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