A modified finite volume element method for solving the phase field Allen–Cahn model. (May 2022) - Li, Huanrong; Wang, Dongmei
Abstract: In this paper, a modified finite volume element (MFVE) method is studied for the nonlinear phase field Allen–Cahn model including a small perturbation parameter. To this end, a traditional finite volume element (FVE) algorithm is firstly proposed to the phase field Allen–Cahn equation and the error estimations of the FVE solutions are derived. After that, a set of optimal basis functions are obtained by using the proper orthogonal decomposition approach, and a MFVE method with the reduced order is established. In particular, the optimal error estimations of the MFVE solutions of the phase field equation are proved. Finally, the theoretical results are verified by numerical tests, which also show that the CPU running time of the MFVE algorithm is much smaller than that of the traditional FVE one.