A moving finite element method for the solution of two-dimensional time-dependent models Original Research Article

In this paper 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.