Profile of Xuefeng LIU (xfliu)

Xuefeng LIU   @ Tokyo Woman's Christian University   HP: http://www.xfliu.org

My research focuses on numerical methods for partial differential equations.

NS.SolutionVerification : Solution verification for the Navier-Stokes equation [Public]

By xfliu  ( )

Demonstration of the solution verification for the Naiver-Stokes equation over 3D domains.

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Hypercircle : The hypercircle method for the error estimation of FEM solutions [Public]

By xfliu  ( )

This project describes how to obtain explicit a priori error estimation for FEM solution by using the hypercircle method.

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StokesEigProblem [Public]

By xfliu  ( )

The eigenvalue estimation for Stokes operator.

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vfem : Verified Finite Element Method Library [Public]

By xfliu  ( )

The Verified Finite Element Method (VFEM) library

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StokesEquation [Public]

By xfliu  ( )

The a priori error estimation for the FEM solution to Stokes equation over 3D domain.

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ProjectConstantCR [Public]

By xfliu  ( )

The projection error constant estimation for Crouzeix-Raviart FEM.

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Matrix4StokesEquation : Matrix generation in solving the Stokes equation by FEM [Public]

By xfliu  ( )

In solving the Stokes equation, one has to consider the solution of linear system under a linear constraint condition. Here, the code is prepared for the matrix generation.

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OctaveInterval : Example of Interval package in Octave [Public]

By xfliu  ( )

The project show several examples about interval computing in Octave.

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eigenproblem-various-domains : Eigenfunction plot various domain [Public]

By xfliu  ( )

Eigenfunction plot various domain

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AIM-Torsion-Problem : AIM Torsion Problem [Public]

By xfliu  ( )

AIM Torsion Problem team

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EigenVecEstimation [Public]

By xfliu  ( )

This project shows a demo of the algorithm of the a posteriori error estimation for eigenvector of eigenvalue problems, such as, the matrix eigenvalue problem, the Laplacian eigenvalue problem.

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discontinuous-hypercircle : Discontinuous coefficient of Poisson's equation with hypercricle [Public]

By xfliu  ( )

The project demonstrate how to use hypercircle method to obtain a posteriori and a priori error estimation for the Poisson equation with non-continuous cofficients.

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EigenfunctionEstimation4FEM : Eigenfunction Estimation based on FEM solutions [Public]

By xfliu  ( )

This project demonstrate the eigenfunction estimation of Laplacian using finite element method.

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FEM-Seminar-2025 : Introduction of FEM packages: FEniCSx and Firedrake [Public]

By xfliu  ( )

Demonstration of FEM packages: FEniCSx and Firedrake in Ganjin Image 2.0.

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Book-GCEVP : Book: Guaranteed computation methods for eigenvalue problems of differential operators [Public]

By xfliu  ( )

The codes for numerical examples in the book: Guaranteed computation methods for eigenvalue problems of differential operators.

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dumbbell_domain : Dumbbell domain [Public]

By xfliu  ( )

eigenvalue problem

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LG-Method : Lehmann-Goerisch Method for high-precision eigenvalue bounds [Public]

By xfliu  ( )

The project demonstrates the high-precision eigenvalue bounds via Lehmann-Goerisch method

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EigenvalueBound : Eigenvalue bounds for Laplacian [Public]

By xfliu  ( )

The explicit lower bound and upper bound for the Laplace differential operator are obtained by using the conforming and non-conforming finite element method.

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