A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation

摘要

Fractional-in-space Allen-Cahn equation containing a very strong nonlinear source term and small perturbation shows metastability and a quartic double well potential.Using a finite volume unstructured triangular mesh method,the present paper solves the two-dimensional fractional-in-space Allen-Cahn equation with homogeneous Neumann boundary condition on different irregular domains.The efficiency of the method is presented throughnumerical computation of the two-dimensional fractional-in-space Allen-Cahn equation ondifferent domains.