A modified finite volume element method for solving the phase field Allen-Cahn model

Article Mathematics, Applied

A reduced-order finite element method based on proper orthogonal decomposition for the Allen-Cahn model

Huanrong Li et al.

Summary: This paper focuses on a reduced-order finite element method for the Allen-Cahn equation. It first derives a traditional finite element formulation and establishes a novel reduced order FE formulation using proper orthogonal decomposition technique. Numerical experiments are provided to confirm the validity of the novel ROFE formulation.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Mathematics, Applied

Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model

Huanrong Li et al.

Summary: This paper proposes a reduced-order finite element method based on the POD technique for simulating the Allen-Cahn phase field model, with error estimates of the solutions provided. Numerical results demonstrate the effectiveness of the proposed method.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2021)

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Article Mathematics, Applied

A reduced-order modified finite difference method preserving unconditional energy-stability for the Allen-Cahn equation

Huanrong Li et al.

Summary: This paper introduces a reduced-order finite difference method with an extra modified term for solving the Allen-Cahn equation with small parameter perturbation and a non-linear term related to energy function. Numerical tests validate the method's effectiveness and demonstrate that it has significantly lower CPU running time compared to traditional finite difference methods.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2021)

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Article Mathematics, Applied