Yanlong Zhang¹, Yanhui Zhou², Jiming Wu^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 487-514, 2021, DOI:10.32604/cmes.2021.014950

Abstract In this article, we study a 2D nonlinear time-fractional Rayleigh-Stokes problem, which has an anomalous sub-diffusion term, on triangular meshes by quadratic finite volume element schemes. Time-fractional derivative, defined by Caputo fractional derivative, is discretized through formula, and a two step scheme is used to approximate the time first-order derivative at time , where the nonlinear term is approximated by using a matching linearized difference scheme. A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization, where the range of values for two parameters are , . For testing the precision of numerical… More >

An Chen^*

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.1, pp. 173-195, 2020, DOI:10.32604/cmes.2020.011871

Abstract In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time. More >

Mengya Su¹, Zhihao Ren¹, Zhiyue Zhang^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 739-776, 2020, DOI:10.32604/cmes.2020.08563

Abstract Based on rectangular partition and bilinear interpolation, we construct an alternating-direction implicit (ADI) finite volume element method, which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients. This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes. Optimal error estimate in L² norm is obtained for the schemes. Compared with the finite volume element method of the same convergence order, our method is more effective in terms of running time with the increasing of the computing scale. Numerical… More >

Andrew Lundberg¹, Pengtao Sun^1,∗, Cheng Wang², Chen-song Zhang³

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 35-62, 2019, DOI:10.32604/cmes.2019.04804

Abstract The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated. More >

Zhendong Luo¹, Fei Teng²

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 33-58, 2014, DOI:10.3970/cmes.2014.101.033

Abstract A semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes… More >

F. Yang¹, C.L. Fu², X.X. Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 19-29, 2014, DOI:10.3970/cmes.2014.100.019

Abstract Numerical differentiation is a classical ill-posed problem. The generalized Tikhonov regularization method is proposed to solve this problem. The error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Numerical examples are presented to illustrate the validity and effectiveness of this method. More >

Quan Zheng², Jing Wang², Jing-ya Li²

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.2, pp. 103-114, 2011, DOI:10.3970/cmes.2011.072.103

Abstract This paper investigates the coupling method of the finite element and the natural boundary element using an elliptic artificial boundary for solving exterior anisotropic problems, and obtains a new error estimate that depends on the mesh size, the location of the elliptic artificial boundary, the number of terms after truncating from the infinite series in the integral. Numerical examples are presented to demonstrate the effectiveness and the properties of this method. More >

Y.Y. Shan¹, C. Shu^1,2, Z.L. Lu³

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.2, pp. 99-114, 2008, DOI:10.3970/cmes.2008.025.099

Abstract The local multiquadric-based differential quadrature (MQ-DQ) method proposed by [Shu, Ding, and Yeo (2003)] is a natural mesh-free approach for derivative approximation, which is easy to be implemented to solve problems with curved boundary. Previously, it has been well tested for the two-dimensional (2D) case. In this work, this mesh-free method was extended to simulate fluid flow problems with curved boundary in three-dimensional (3D) space. The main concern of this work is to numerically study the performance of the 3D local MQ-DQ method and demonstrate its capability and flexibility for simulation of 3D incompressible fluid flows with curved boundary. Fractional… More >

Chein-ShanLiu¹

CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 219-234, 2009, DOI:10.3970/cmc.2009.013.219

Abstract The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the new method. More >