Article
Mathematics, Applied
Xixian Bai, Hongxing Rui
Summary: This paper introduces new energy identities for metamaterial Maxwell's equations with PEC boundary conditions, different from the Poynting theorem. It is proved that the Yee scheme remains stable on non-uniform rectangular meshes when the CFL condition is met. Numerical experiments confirm the analysis and reveal superconvergence in the discrete H-1 norm.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2021)
Article
Mathematics, Applied
Lixiu Wang, Qian Zhang, Zhimin Zhang
Summary: In this paper, we provide a theoretical justification for the previously observed superconvergence phenomena of the curlcurl-conforming finite elements on rectangular domains. We establish a superconvergence theory for these elements on rectangular meshes and show that the convergence rates are one-order higher than the optimal rates. Numerical experiments are conducted to confirm our theoretical results.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
C. Wu, H. Zeng, Y. Huang, N. Yi, J. Yuan
Summary: This article introduces a new recovery method for curl conforming elements on cuboid mesh, achieving superconvergence of recovered edge finite element solution by exploiting symmetry. Theoretical findings are validated through numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Hardware & Architecture
Mohammad Javidi, Mahdi Saedshoar Heris
Summary: In this paper, algorithms using piecewise linear interpolation polynomial are designed and developed to solve partial fractional differential equations involving Caputo derivative. The algorithms are applied to both uniform and non-uniform meshes, and new methods for selecting mesh points are proposed. Error bounds for the proposed methods with uniform and equidistributing meshes are obtained. The numerical method is stable and convergent with an accuracy of O(kappa(2) + h), as demonstrated through numerical examples and a comparative study for different parameter values.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Mathematics, Applied
Chao Wu, Yunqing Huang, Nianyu Yi, Huayi Wei, Jinyun Yuan
Summary: This paper proposes function and curl recovery methods for the lowest order triangular edge element, and carries out a superconvergence analysis and numerical experiments to validate the effectiveness of the methods.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Waixiang Cao, Lueling Jia, Zhimin Zhang
Summary: This paper designs and analyzes a new C-1-conforming Petrov-Galerkin method for convection-diffusion equations. The existence and uniqueness of the numerical solution are proved, and optimal error estimates in the L-2-, H-1-, and H-2-norms are shown. Furthermore, the superconvergence properties of the new method are established, and superconvergence points/lines are identified at various locations. Interior a priori error estimates in the L-2-, H-1-, and H-2-norms are derived to reduce the global regularity requirement. Numerical experiments are conducted to validate the theoretical findings.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Nuodi Liu, Yanping Chen, Jianwei Zhou, Yunqing Huang
Summary: In this paper, a mixed finite element method (MFEM) is developed for solving the time-dependent Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium. The unconditional stability of the fully discrete backward Euler scheme is proven, and global superconvergence results are obtained using interpolation postprocessing techniques. Numerical experiments in two dimensions are provided to demonstrate the validity of the theoretical analysis, which has not been discussed in any other publications.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Mohammad Javidi, Mahdi Saedshoar Heris
Summary: This paper introduces efficient numerical schemes for solving the time fractional Fokker-Planck equation with the predictor-corrector approach and method of lines, demonstrating both effectiveness and accuracy.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Alexander Zlotnik, Raimondas Ciegis
Summary: The study examines the necessary conditions for stability of a Numerov-type compact higher-order finite-difference scheme for the 1D homogeneous wave equation on non-uniform spatial meshes. It is found that exponential growth in solution norm and excessively strong conditions between time and space steps are required for stability, even in the case of non-uniform time stability.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Xiaoli Li, Hongxing Rui
Summary: This paper presents a marker and cell (MAC) scheme for the free flow-porous media system with heat transport on non-uniform grids, utilizing the Stokes-Darcy equation to describe the flow in both free-flow and porous regions. Rigorous error estimates for velocity, pressure, and temperature in different discrete norms are established through the construction of discrete auxiliary functions. The study demonstrates second-order superconvergence in the discrete L-2 norm for velocity, pressure, and temperature, as well as second-order superconvergence for certain terms of the H-1 norm for velocity on non-uniform grids.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Yanli Chen, Xue Jiang, Jun Lai, Peijun Li
Summary: This paper investigates the three-dimensional electromagnetic scattering from a large open rectangular cavity embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary condition and utilizing a fast algorithm involving fast Fourier transform and Gaussian elimination, the paper solves the linear system for cavities filled with either a homogeneous or layered medium, demonstrating superior performance in numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Leijie Qiao, Wenlin Qiu, Da Xu
Summary: This study constructs and analyzes a nonlocal evolution equation with a weakly singular kernel in three-dimensional space, using different numerical methods to ensure stability and convergence. The numerical results confirm the theoretical analysis.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Yunqing Huang, Jichun Li, Xuancen Yi, Haoke Zhao
Summary: In this paper, a finite element method (FEM) is developed and analyzed for the Drude perfectly matched layer (PML) model. The stability analysis and error estimate for the scheme are established. Numerical results demonstrate the effectiveness of this PML in absorbing outgoing waves in the Drude metamaterial.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Minqiang Xu, Kai Liu, Lei Zhang
Summary: In this paper, a staggered finite volume element method (FVEM) based marker and cell method (MAC) is proposed for solving 3D Stokes equations on non-uniform cuboid grids with a proper quadrature scheme. The stability of the proposed MAC scheme is proven using the Petrov-Galerkin method. By establishing a connection between MAC and FVEM, the superconvergence property and optimal order L2 error estimate are rigorously proved. Numerical results are provided to verify the theoretical findings.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Jie Gu, Lijuan Nong, Qian Yi, An Chen
Summary: In this paper, the authors propose effective numerical schemes for the time-fractional Black-Scholes equation. The original equation is converted into an equivalent integral-differential equation and discretized using piecewise linear interpolation for the time-integral term and compact difference formula for the spatial direction. The derived fully discrete compact difference scheme demonstrates second-order accuracy in time and fourth-order accuracy in space, with rigorous proofs of stability and convergence. Furthermore, the authors extend the results to non-uniform meshes for dealing with non-smooth solutions and provide a temporal non-uniform mesh-based compact difference scheme.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Ming Sun, Jichun Li, Peizhen Wang, Zhimin Zhang
JOURNAL OF SCIENTIFIC COMPUTING
(2018)
Article
Mathematics, Applied
Jichun Li, Meng Chen, Min Chen
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2019)
Article
Engineering, Multidisciplinary
Yunqing Huang, Jichun Li, Chao Wu
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2018)
Article
Engineering, Multidisciplinary
Jichun Li, Zhiwei Fang, Guang Lin
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2018)
Article
Mathematics, Applied
Yunqing Huang, Meng Chen, Jichun Li, Yanping Lin
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Article
Mathematics, Applied
Yunqing Huang, Hongen Jia, Jichun Li
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2018)
Article
Mathematics, Applied
Xiaofeng Jia, Jichun Li, Hongen Jia
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Jichun Li, Chen Meng, Yunqing Huang
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Hongen Jia, Jichun Li, Zhiwei Fang, Ming Li
NUMERICAL ALGORITHMS
(2019)
Article
Mathematics, Applied
Sean Breckling, Sidney Shields
APPLIED MATHEMATICS AND COMPUTATION
(2019)
Article
Mathematics, Applied
Zhiwei Fang, Jichun Li, Tao Tang, Tao Zhou
JOURNAL OF SCIENTIFIC COMPUTING
(2019)
Article
Mathematics, Applied
Yunqing Huang, Jichun Li, Shangyou Zhang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
Proceedings Paper
Engineering, Electrical & Electronic
Sidney Shields, Jichun Li
2018 PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM (PIERS-TOYAMA)
(2018)
Proceedings Paper
Engineering, Electrical & Electronic
Meng Chen, Yunqing Huang, Jichun Li
2018 PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM (PIERS-TOYAMA)
(2018)
Article
Mathematics, Applied
Jichun Li, Zhiwei Fang
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2018)