In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,...In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.展开更多
基金partially supported by the National Natural Science Foundation of China(Grant No.12261070)the Ningxia Key Research and Development Project of China(Grant No.2022BSB03048)+2 种基金partially supported by the Simons(Grant No.633724)and by Fundacion Seneca grant 21760/IV/22partially supported by the Spanish national research project PID2019-108336GB-I00by Fundacion Séneca grant 21728/EE/22.Este trabajo es resultado de las estancias(21760/IV/22)y(21728/EE/22)financiadas por la Fundacion Séneca-Agencia de Ciencia y Tecnologia de la Region de Murcia con cargo al Programa Regional de Movilidad,Colaboracion Internacional e Intercambio de Conocimiento"Jimenez de la Espada".(Plan de Actuacion 2022).
文摘In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.
