| THE LOWER APPROXIMATION OF EIGENVALUE BY LUMPED MASS FINITE ELEMENT METHOD |
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| 作者姓名： | JunHu Yun-qingHuang HongmeiShen |
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| 作者单位： | DepartmentofMathematics,XiangtanUniversity,XiangtanJ11105,China |
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| 基金项目： | Subsidized by special fund for state major basic research projects and state educational ministry. |
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| 摘 要： | In the present paper, we investigate properties of lumped mass finite element method (LFEM hereinafter) eigenvalues of elliptic problems. We propose an equivalent formulation of LFEM and prove that LFEM eigenvalues are smaller than the standard finite element method (SFEM hereinafter) eigenvalues. It is shown, for model eigenvalue problems with uniform meshes, that LFEM eigenvalues are not greater than exact solutions and that they are increasing functions of the number of elements of the triangulation, and numerical examples show that this result equally holds for general problems.
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| 关 键 词： | 特征值 集中质量 有限元法 运算法则 |
THE LOWER APPROXIMATION OF EIGENVALUE BY LUMPED MASS FINITE ELEMENT METHOD |
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| JunHu Yun-qingHuang HongmeiShen.THE LOWER APPROXIMATION OF EIGENVALUE BY LUMPED MASS FINITE ELEMENT METHOD[J].Journal of Computational Mathematics,2004,22(4):545-556. |
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| Authors: | Jun Hu Yun-qing Huang Hongmei Shen |
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| Institution: | Jun Hu,Yun-qing Huang,Hongmei Shen Department of Mathematics,Xiangtan University,Xiangtan 411105,China |
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| Abstract: | In the present paper,we investigate properties of lumped mass finite element method(LFEM hereinafter)eigenvalues of elliptic problems.We propose an equivalent formulationof LFEM and prove that LFEM eigenvalues are smaller than the standard finite elementmethod(SFEM hereinafter)eigenvalues.It is shown,for model eigenvalue problems withuniform meshes,that LFEM eigenvalues are not greater than exact solutions and thatthey are increasing functions of the number of elements of the triangulation,and numericalexamples show that this result equally holds for general problems. |
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| Keywords: | Lumped mass Eigenvalue Min-max principle Finite element |
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