The Experts below are selected from a list of 76323 Experts worldwide ranked by ideXlab platform
Yifa Tang - One of the best experts on this subject based on the ideXlab platform.
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superconvergence analysis of fem for 2d multi term time fractional diffusion wave equations with variable coefficient
International Journal of Computer Mathematics, 2020Co-Authors: Yanhua Shi, Yanmin Zhao, Fenling Wang, Yifa TangAbstract:The goal of this paper is to discuss high accuracy analysis of a fully-Discrete Scheme for 2D multi-term time fractional wave equations with variable coefficient on anisotropic meshes by approximat...
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convergence and superconvergence of a fully Discrete Scheme for multi term time fractional diffusion equations
Science & Engineering Faculty, 2016Co-Authors: Yanmin Zhao, Yifa Tang, Yadong Zhang, Fawang Liu, Ian Turner, Vo AnhAbstract:Using finite element method in spatial direction and classical L1L1 approximation in temporal direction, a fully-Discrete Scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate Scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h2+τ2−α)O(h2+τ2−α) for the original variable in H1H1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where hh and ττ are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results.
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galerkin finite element method for two dimensional riesz space fractional diffusion equations
Journal of Computational Physics, 2014Co-Authors: Weiping Bu, Yifa Tang, Jiye YangAbstract:Abstract In this article, a class of two-dimensional Riesz space fractional diffusion equations is considered. Some fractional spaces are established and some equivalences between fractional derivative spaces and fractional Sobolev space are presented. By the Galerkin finite element method and backward difference method, a fully Discrete Scheme is obtained. According to Lax–Milgram theorem, the existence and uniqueness of the solution to the fully Discrete Scheme are investigated. The stability and convergence of the Scheme are also derived. Finally, some numerical examples are given for verification of our theoretical analysis.
Antoine Hocquet - One of the best experts on this subject based on the ideXlab platform.
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A semi-Discrete Scheme for the stochastic Landau–Lifshitz equation
Stochastic Partial Differential Equations: Analysis and Computations, 2014Co-Authors: François Alouges, Anne Bouard, Antoine HocquetAbstract:We propose a new convergent time semi-Discrete Scheme for the stochastic Landau–Lifshitz–Gilbert equation. The Scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the Scheme up to a subsequence.
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A semi-Discrete Scheme for the stochastic Landau-Lifshitz equation
Stochastic Partial Differential Equations: Analysis and Computations, 2014Co-Authors: François Alouges, Anne Bouard, Antoine HocquetAbstract:We propose a new convergent time semi-Discrete Scheme for the stochastic Landau-Lifshitz-Gilbert equation. The Scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the Scheme up to a subsequence.
Nicolas Seguin - One of the best experts on this subject based on the ideXlab platform.
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A stiffly stable semi-Discrete Scheme for the characteristic linear hyperbolic relaxation with boundary
ESAIM: Mathematical Modelling and Numerical Analysis, 2020Co-Authors: Benjamin Boutin, Thi Hoai Thuong Nguyen, Nicolas SeguinAbstract:We study the stability of the semi-Discrete central Scheme for the linear damped wave equation with boundary. We exhibit a sufficient condition on the boundary to guarantee the uniform stability of the initial boundary value problem for relaxation system independent of stiffness of the source term and of the space step. The boundary is approximated using a summation-by-parts method and the stiff stability is proved by energy estimates and Laplace transform. We also investigate if the condition is also necessary, following the continuous case studied by Xin and Xu (2000).
Anne Bouard - One of the best experts on this subject based on the ideXlab platform.
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A semi-Discrete Scheme for the stochastic Landau–Lifshitz equation
Stochastic Partial Differential Equations: Analysis and Computations, 2014Co-Authors: François Alouges, Anne Bouard, Antoine HocquetAbstract:We propose a new convergent time semi-Discrete Scheme for the stochastic Landau–Lifshitz–Gilbert equation. The Scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the Scheme up to a subsequence.
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A semi-Discrete Scheme for the stochastic Landau-Lifshitz equation
Stochastic Partial Differential Equations: Analysis and Computations, 2014Co-Authors: François Alouges, Anne Bouard, Antoine HocquetAbstract:We propose a new convergent time semi-Discrete Scheme for the stochastic Landau-Lifshitz-Gilbert equation. The Scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the Scheme up to a subsequence.
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a semi Discrete Scheme for the stochastic nonlinear schrodinger equation
Numerische Mathematik, 2004Co-Authors: Anne Bouard, Arnaud DebusscheAbstract:We study the convergence of a semi-discretized version of a numerical Scheme for a stochastic nonlinear Schrodinger equation. The nonlinear term is a power law and the noise is multiplicative with a Stratonovich product. Our Scheme is implicit in the deterministic part of the equation as is usual for conservative equations. We also use an implicit discretization of the noise which is better suited to Stratonovich products. We consider a subcritical nonlinearity so that the energy can be used to obtain an a priori estimate. However, in the semi Discrete case, no Ito formula is available and we have to use a Discrete form of this tool. Also, in the course of the proof we need to introduce a cut-off of the diffusion coefficient, which allows to treat the nonlinearity. Then, we prove convergence by a compactness argument. Due to the presence of noise and to the implicit discretization of the noise, this is rather complicated and technical. We finally obtain convergence of the Discrete solutions in various topologies.
Jiye Yang - One of the best experts on this subject based on the ideXlab platform.
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galerkin finite element method for two dimensional riesz space fractional diffusion equations
Journal of Computational Physics, 2014Co-Authors: Weiping Bu, Yifa Tang, Jiye YangAbstract:Abstract In this article, a class of two-dimensional Riesz space fractional diffusion equations is considered. Some fractional spaces are established and some equivalences between fractional derivative spaces and fractional Sobolev space are presented. By the Galerkin finite element method and backward difference method, a fully Discrete Scheme is obtained. According to Lax–Milgram theorem, the existence and uniqueness of the solution to the fully Discrete Scheme are investigated. The stability and convergence of the Scheme are also derived. Finally, some numerical examples are given for verification of our theoretical analysis.