首页|A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

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In this paper,a new finite element and finite difference(FE-FD)method has been devel-oped for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P1 FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the inter-face,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 sec-ond order convergence.

Anisotropic parabolic interface problemHybrid finite element and finite difference(FE-FD)discretizationModified Crank-Nicolson scheme

Baiying Dong、Zhilin Li、Juan Ruiz-álvarez

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School of Civil and Hydraulic Engineering,NingXia University,Yinchuan 750021,Ningxia,China

School of Mathematics and Computer Science,NingXia Normal University,Guyuan 756000,Ningxia,China

Department of Mathematics,North Carolina State University,Raleigh,NC 27695-8205,USA

Departamento de Matemática Aplicada y Estadística,Universidad Politécnica de Cartagena,Cartagena,Spain

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National Natural Science Foundation of ChinaNingxia Key Research and Development Project of ChinaSimonsFundación Séneca grantSpanish national research projectFundación Séneca grantFundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad,ColaboraciónFundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad,Colaboración

122610702022BSB0304863372421760/IV/22PID2019-108336GB-I0021728/EE/2221760/IV/2221728/EE/22

2024

10.1007/s42967-023-00281-x

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子：0.165
ISSN：1006-6330
年,卷(期)：2024.6(2)