Public projects

SSP2025-Lecture : The hypercircle method for the error estimation of FEM solutions (Clone from xfliu/Hypercircle) [Public]

By Xuefeng LIU (2025-02-10T07:05:11Z )

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

1D-FEM : 1D-FEM [Public]

By kaoru (2021-07-11T04:33:56Z )

領域の両端で０となる1次元のPoisson方程式を解く有限要素法プログラム

2D-FEM-Intro : 2D-FEM-Intro : 2次元有限要素法入門 [Public]

By kaoru (2021-07-11T06:02:24Z )

正方領域における有限要素法の入門コード FEniCSによる解析を軸に基礎理論について紹介している。

Deflection : Deflection [Public]

By kaoru (2020-09-11T07:51:06Z )

たわみを文字式のまま解く

Hypercircle : Steklov Eigenvalue [Public]

By liqin (2020-11-17T02:50:24Z )

By using the hypercircle method, this project describes how to obtain the guareenteed lower eigenvalue bound of Steklov operator with FEM.

EigenfunctionEstimation4FEM : Eigenfunction Estimation based on FEM solutions (Clone from xfliu/EigenfunctionEstimation4FEM) [Public]

By mahdipc (2023-03-11T11:59:31Z )

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

SSP2025-Lecture : The hypercircle method for the error estimation of FEM solutions [Public]

By movemesh (2025-02-10T07:09:07Z )

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

Guaranteed_local_error_estimation : Local error estimation in JCAM [Public]

By nakano (2023-01-11T01:48:55Z )

This project provides a numerical example shown in the following article: https://www.sciencedirect.com/science/article/pii/S0377042723000055

Guaranteed_error_estimation_for_modified_Helmholtz_eq : Guaranteed_error_estimation_for_modified_Helmholtz_eq [Public]

By nakano (2023-02-21T00:48:32Z )

This project provides computational examples related to guaranteed error estimation for the modified Helmholtz equations. The computation method used in this project is based on the approach presented in the research paper available at arxiv.org:2001.09820, as well as the project available at https://ganjin.online/liqin/Hypercircle.

singularity : dumbbell-shaped-domain [Public]

By ryoki (2023-06-18T06:30:04Z )

ShapeDerivativeEstimation : Rigorous shape derivative of eigenvalues estimation [Public]

By ryoki (2022-09-28T14:05:34Z )

This project demonstrates an implementation of the algorithms proposed in "Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation".

DirichletSimplicity : the 2nd and 3rd eigenvalues on triangles [Public]

By ryoki (2024-03-22T00:52:13Z )

Computer-assisted proof for the simplicity of the 2nd and 3rd dirichlet eigenvalues on triangular domains

DirichletSimplicityCollapse : Simplicity of the 2nd and 3rd eigenvalues over collapsing triangles [Public]

By ryoki (2025-03-10T22:07:07Z )

Computer-assisted proof for the simplicity of the 2nd and 3rd Dirichlet eigenvalues on nearly degenerate triangles

eigen-pedia : Eigenfunction Encyclopedia [Public]

By ryoki (2024-11-18T06:19:27Z )

EigenOpt_Triangles : Eigenvalue Optimization Over Triangles [Public]

By ryoki (2025-02-07T22:19:46Z )

InterpolationErrorEstimate : Interpolation error estimate [Public]

By shirley (2022-05-26T13:58:54Z )

Demonstration of the method of estimating the upper bound of the constant for the maximum norm of the Lagrange interpolation error.

Pointwise : Pointwise (Clone from nakano/Pointwise) [Public]

By shirley (2022-06-08T11:43:07Z )

Pointwise error estimation based on the Fujita method for the Poisson BVP.

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

By xfliu (2025-02-22T03:29:21Z )

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

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

By xfliu (2024-03-11T08:28:19Z )

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

StokesEigProblem [Public]

By xfliu (2020-07-11T17:11:46Z )

The eigenvalue estimation for Stokes operator.

vfem : Verified Finite Element Method Library [Public]

By xfliu (2021-09-18T16:06:49Z )

The Verified Finite Element Method (VFEM) library

StokesEquation [Public]

By xfliu (2021-07-11T05:30:24Z )

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

ProjectConstantCR [Public]

By xfliu (2020-07-04T13:37:25Z )

The projection error constant estimation for Crouzeix-Raviart FEM.

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

By xfliu (2022-10-05T08:32:29Z )

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.

OctaveInterval : Example of Interval package in Octave [Public]

By xfliu (2021-01-01T01:06:29Z )

The project show several examples about interval computing in Octave.

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

By xfliu (2024-01-11T13:26:58Z )

Eigenfunction plot various domain

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

By xfliu (2024-06-21T23:29:42Z )

AIM Torsion Problem team

EigenVecEstimation [Public]

By xfliu (2020-05-14T05:47:02Z )

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.

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

By xfliu (2024-09-15T01:08:34Z )

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.

EigenfunctionEstimation4FEM : Eigenfunction Estimation based on FEM solutions [Public]

By xfliu (2023-02-09T20:59:28Z )

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

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

By xfliu (2025-02-24T14:47:13Z )

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

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

By xfliu (2023-05-04T15:49:49Z )

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

veig : Verified Eigenvalue Computation for Matrices [Public]

By xfliu (2025-06-27T09:34:50Z )

Verified Eigenvalue Computation for Matrices

dumbbell_domain : Dumbbell domain [Public]

By xfliu (2024-10-05T04:09:59Z )

eigenvalue problem

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

By xfliu (2025-03-24T05:32:43Z )

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

EigenvalueBound : Eigenvalue bounds for Laplacian [Public]

By xfliu (2023-04-25T16:25:45Z )

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

All public projects

SSP2025-Lecture : The hypercircle method for the error estimation of FEM solutions (Clone from xfliu/Hypercircle) [Public]

1D-FEM : 1D-FEM [Public]

2D-FEM-Intro : 2D-FEM-Intro : 2次元有限要素法入門 [Public]

Deflection : Deflection [Public]

Hypercircle : Steklov Eigenvalue [Public]

EigenfunctionEstimation4FEM : Eigenfunction Estimation based on FEM solutions (Clone from xfliu/EigenfunctionEstimation4FEM) [Public]

SSP2025-Lecture : The hypercircle method for the error estimation of FEM solutions [Public]

Guaranteed_local_error_estimation : Local error estimation in JCAM [Public]

Guaranteed_error_estimation_for_modified_Helmholtz_eq : Guaranteed_error_estimation_for_modified_Helmholtz_eq [Public]

singularity : dumbbell-shaped-domain [Public]

ShapeDerivativeEstimation : Rigorous shape derivative of eigenvalues estimation [Public]

DirichletSimplicity : the 2nd and 3rd eigenvalues on triangles [Public]

DirichletSimplicityCollapse : Simplicity of the 2nd and 3rd eigenvalues over collapsing triangles [Public]

eigen-pedia : Eigenfunction Encyclopedia [Public]

EigenOpt_Triangles : Eigenvalue Optimization Over Triangles [Public]

InterpolationErrorEstimate : Interpolation error estimate [Public]

Pointwise : Pointwise (Clone from nakano/Pointwise) [Public]

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

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

StokesEigProblem [Public]

vfem : Verified Finite Element Method Library [Public]

StokesEquation [Public]

ProjectConstantCR [Public]

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

OctaveInterval : Example of Interval package in Octave [Public]

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

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

EigenVecEstimation [Public]

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

EigenfunctionEstimation4FEM : Eigenfunction Estimation based on FEM solutions [Public]

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

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

veig : Verified Eigenvalue Computation for Matrices [Public]

dumbbell_domain : Dumbbell domain [Public]

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

EigenvalueBound : Eigenvalue bounds for Laplacian [Public]