The Experts below are selected from a list of 7242 Experts worldwide ranked by ideXlab platform
Shaochun Chen - One of the best experts on this subject based on the ideXlab platform.
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the nonconforming virtual element method for fourth order Singular Perturbation Problem
Advances in Computational Mathematics, 2020Co-Authors: Bei Zhang, Jikun Zhao, Shaochun ChenAbstract:We present the nonconforming virtual element method for the fourth-order Singular Perturbation Problem. The virtual element proposed in this paper is a variant of the C0-continuous nonconforming virtual element presented in our previous work and allows to compute two different projection operators that are used for the construction of the discrete scheme. We show the optimal convergence in the energy norm for the nonconforming virtual element method. Further, the lowest order nonconforming method is proved to be uniformly convergent with respect to the Perturbation parameter. Finally, we verify the convergence for the nonconforming virtual element method by some numerical tests.
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uniformly convergent c 0 nonconforming triangular prism element for fourth order elliptic Singular Perturbation Problem
Numerical Methods for Partial Differential Equations, 2014Co-Authors: Hongru Chen, Shaochun Chen, Liuchao XiaoAbstract:In this article, we introduce a C 0-nonconforming triangular prism element for the fourth-order elliptic Singular Perturbation Problem in three dimensions by using the bubble functions. The element is proved to be convergent in the energy norm uniformly with respect to the Perturbation parameter. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1785–1796, 2014
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uniformly convergent nonconforming element for 3 d fourth order elliptic Singular Perturbation Problem
Journal of Computational Mathematics, 2014Co-Authors: Hongru Chen, Shaochun ChenAbstract:In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic Singular Perturbation Problem in three dimensions. We prove that the nonconforming C 0 -cuboid element converges in the energy norm uniformly with respect to the Perturbation parameter. Mathematics subject classification: 65N12, 65N30.
Hongru Chen - One of the best experts on this subject based on the ideXlab platform.
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uniformly convergent c 0 nonconforming triangular prism element for fourth order elliptic Singular Perturbation Problem
Numerical Methods for Partial Differential Equations, 2014Co-Authors: Hongru Chen, Shaochun Chen, Liuchao XiaoAbstract:In this article, we introduce a C 0-nonconforming triangular prism element for the fourth-order elliptic Singular Perturbation Problem in three dimensions by using the bubble functions. The element is proved to be convergent in the energy norm uniformly with respect to the Perturbation parameter. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1785–1796, 2014
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uniformly convergent nonconforming element for 3 d fourth order elliptic Singular Perturbation Problem
Journal of Computational Mathematics, 2014Co-Authors: Hongru Chen, Shaochun ChenAbstract:In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic Singular Perturbation Problem in three dimensions. We prove that the nonconforming C 0 -cuboid element converges in the energy norm uniformly with respect to the Perturbation parameter. Mathematics subject classification: 65N12, 65N30.
Zhongyi Huang - One of the best experts on this subject based on the ideXlab platform.
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tailored finite point method for a Singular Perturbation Problem with variable coefficients in two dimensions
Journal of Scientific Computing, 2009Co-Authors: Houde Han, Zhongyi HuangAbstract:In this paper, we propose a tailored-finite-point method for a type of linear Singular Perturbation Problem in two dimensions. Our finite point method has been tailored to some particular properties of the Problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ?, i.e. the boundary layers and interior layers do not need to be resolved numerically. In our numerical implementation, we study the classification of all the Singular points for the corresponding degenerate first order linear dynamic system. We also study some cases with nonlinear coefficients. Our tailored finite point method is very efficient in both linear and nonlinear coefficients cases.
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a tailored finite point method for a Singular Perturbation Problem on an unbounded domain
Journal of Scientific Computing, 2008Co-Authors: Houde Han, Zhongyi Huang, Bruce R KelloggAbstract:In this paper, we propose a tailored-finite-point method for a kind of Singular Perturbation Problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original Problem to a Problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced Problem, where our finite point method has been tailored to some particular properties or solutions of the Problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small ?. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh.
Sergei Kuksin - One of the best experts on this subject based on the ideXlab platform.
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a kam theorem for space multidimensional hamiltonian pde
arXiv: Analysis of PDEs, 2016Co-Authors: Hakan L Eliasson, Benoit Grebert, Sergei KuksinAbstract:We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: $\bullet$ the integrable part of the hamiltonian may contain a hyperbolic part and as a consequence the constructed invariant tori may be unstable. $\bullet$ It applies to Singular Perturbation Problem. In this paper we state the KAM-theorem and comment on it, give the main ingredients of the proof, and present three applications of the theorem .
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a kam theorem for space multidimensional hamiltonian pde
Proceedings of the Steklov Institute of Mathematics, 2016Co-Authors: Hakan L Eliasson, Benoit Grebert, Sergei KuksinAbstract:We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: • the integrable part of the hamiltonian may contain a hyperbolic part and as a consequence the constructed invariant tori may be unstable. • It applies to Singular Perturbation Problem. In this paper we state the KAM-theorem and comment on it, give the main ingredients of the proof, and present three applications of the theorem .
Dongyang Shi - One of the best experts on this subject based on the ideXlab platform.
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uniform superconvergent analysis of a new mixed finite element method for nonlinear bi wave Singular Perturbation Problem
Applied Mathematics Letters, 2019Co-Authors: Dongyang ShiAbstract:Abstract Uniform superconvergent analysis of a new low order nonconforming mixed finite element method (MFEM) is studied for solving the fourth order nonlinear Bi-wave Singular Perturbation Problem (SPP) by E Q 1 r o t element. On one hand, the existence, uniqueness and stability of the numerical solutions are proved. On the other hand, with the help of the special characters of this element, uniform superclose result of order O ( h 2 ) for the original variable in the broken H 1 norm and uniform optimal order estimate of order O ( h 2 ) for the intermediate variable in L 2 norm are deduced irrelevant to the real Perturbation parameter δ appearing in the considered Problem, respectively. In which, the nonlinear term in the Bi-wave SPP, which is the main difficulty in the whole error analysis, is dealt with rigorously through a novel splitting technique. Moreover, the global uniform superconvergent estimate is obtained with the interpolated postprocessing approach. Finally, some numerical results are provided to confirm the theoretical analysis. Here h is the subdivision parameter.
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a new robust c0 type nonconforming triangular element for Singular Perturbation Problems
Applied Mathematics and Computation, 2010Co-Authors: Pingli Xie, Dongyang ShiAbstract:Abstract In this paper, a new robust C 0 triangular element is proposed for the fourth order elliptic Singular Perturbation Problem with double set parameter method and bubble function technique, and a general convergence theorem for C 0 nonconforming elements is presented. The convergence of the new element is proved in the energy norm uniformly with respect to the Perturbation parameter. Numerical experiments are also carried out to demonstrate the efficiency of the new element.
