Gradient recovery based finite element methods for the two-dimensional quad-curl problem

Article Mathematics, Applied

A C0 linear finite element method for a second-order elliptic equation in non-divergence form with Cordes coefficients

Minqiang Xu et al.

Summary: In this paper, a gradient recovery based linear finite element method (GRBL FEM) and a Hessian recovery based linear FEM are developed for solving second-order elliptic equations in non-divergence form. The proposed methods are competitive and can handle computational domains with curved boundaries without loss of accuracy.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2023)

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Article Mathematics, Applied

A Hessian recovery-based finite difference method for biharmonic problems

Minqiang Xu et al.

Summary: In this paper, a new finite difference method for biharmonic equations is studied by combining Hessian recovery techniques and the ghost points method. Numerical results validate the optimal convergence orders of the proposed method in the L2 norm and H1 seminorm. Moreover, superconvergence properties of the recovered gradient and Hessian have been observed.

APPLIED MATHEMATICS LETTERS (2023)

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Article Engineering, Multidisciplinary

An efficient technique based on least-squares method for fractional integro-differential equations

Yuntao Jia et al.

Summary: In this paper, an efficient technique for solving fractional integro-differential equations (FIDEs) is investigated, which has numerous applications in various fields of science. The proposed technique is based on the Legendre orthonormal polynomial and least squares method (LSM). By dividing the domain into cells, a polynomial approximate solution can be obtained in each cell by LSM. The solvability and stability of the proposed numerical scheme are proven, and the optimal convergence order under W22-norm is provided. Numerical examples verify the theoretical discovery and show the superiority of the proposed algorithm compared to traditional methods.

ALEXANDRIA ENGINEERING JOURNAL (2023)

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Article Mathematics, Applied

A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampere equation

Hongtao Chen et al.

Summary: This paper presents a new recovery-based linear C-0 finite element method for approximating the weak solution of a fourth-order singularly perturbed Monge-Ampere equation, establishing its uniqueness and deriving error estimates.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2021)

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Article Mathematics, Applied