Yazar "Zhu, Peng" seçeneğine göre listele

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    Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms
    (Elsevier, 2023) Toprakseven, Şuayip; Zhu, Peng
    A weak Galerkin finite element method is proposed for solving singularly perturbed problems with two parameters. A robust uniform optimal convergence has been proved in the corresponding energy and a stronger balanced norms using piecewise higher order discontinuous polynomials on a piecewise uniform Shishkin mesh. Finally, we give some numerical experiments to support theoretical results.
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    A parameter-uniform weak Galerkin finite element method for a coupled system of singularly perturbed reaction-diffusion equations
    (Faculty of Sciences and Mathematics, University of Nis, Serbia, 2023) Toprakseven, Şuayip; Zhu, Peng
    The aim of this paper to investigate a weak Galerkin finite element method (WG-FEM) for solving a system of coupled singularly perturbed reaction-diffusion equations. Each equation in the system has perturbation parameter of different magnitude and thus, the solutions will exhibit two distinct but overlapping boundary layers near each boundary of the domain. The proposed method is applied to the coupled system on Shishkin mesh to solve the problem theoretically and numerically. Elimination of the interior unknowns efficiently from the discrete solution system reduces the degrees of freedom and, thus the number of unknown in the discrete solution is comparable with the standard finite element scheme. The stability and error analysis of the proposed method on the Shishkin mesh are presented. We show that the method convergences of order O(N?k lnk N) in the energy norm, uniformly with respect to the perturbation parameter. Moreover, the optimal convergence rate of O(N?(k+1)) in the L 2 -norm and the superconvergence rate of O((N?2k ln2k N) in the discrete L ?-norm is observed numerically. Finally, some numerical experiments are carried out to verify numerically theory.
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    Uniform convergent modified weak Galerkin method for convection-dominated two-point boundary value problems
    (Scientific Technical Research Council Turkey-Tubitak, 2021) Toprakseven, Şuayip; Zhu, Peng
    We propose and analyze a modified weak Galerkin finite element method (MWG-FEM) for solving singularly perturbed problems of convection-dominated type. The proposed method is constructed over piecewise polynomials of degree k >= 1 on interior of each element and piecewise constant on the boundary of each element. The present method is parameter-free and has less degrees of freedom compared to the classical weak Galerkin finite element method. The method is shown uniformly convergent for small perturbation parameters. An uniform convergence rate of O((N(-1)ln N)(k)) in the energy-like norm is established on the piecewise uniform Shishkin mesh, where N is the number of elements. Various numerical examples are presented to confirm the theoretical results. Moreover, we numerically confirm that the proposed method has the optimal order error estimates of O(N-(k+1)) in a discrete L-2-norm and converges at superconvergence order of O((N(-1)ln N)(2k)) in the discrete L-infinity-norm.