The Experts below are selected from a list of 24726 Experts worldwide ranked by ideXlab platform
Ian Turner - One of the best experts on this subject based on the ideXlab platform.
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an unstructured mesh finite element method for solving the multi term time fractional and riesz space distributed order wave equation on an irregular Convex Domain
Applied Mathematical Modelling, 2019Co-Authors: Y M Zhao, F.l. Wang, Ian TurnerAbstract:Abstract In this paper, the numerical analysis for a multi-term time fracstional and Riesz space distributed-order wave equation is discussed on an irregular Convex Domain. Firstly, the equation is transformed into a multi-term time-space fractional wave equation using the mid-point quadrature rule to approximate the distributed-order Riesz space derivative. Next, the equation is solved by discretising in time using a Crank–Nicolson scheme and in space using the finite element method (FEM) with an unstructured mesh, respectively. Furthermore, stability and convergence are investigated by introducing some important lemmas on irregular Convex Domain. Finally, some examples are provided to show the effectiveness and correctness of the proposed numerical method.
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a novel unstructured mesh finite element method for solving the time space fractional wave equation on a two dimensional irregular Convex Domain
Fractional Calculus and Applied Analysis, 2017Co-Authors: Xiaoyun Jiang, Ian TurnerAbstract:Most existing research on applying the finite element method to discretize space fractional operators is studied on regular Domains using either uniform structured triangular meshes, or quadrilateral meshes. Since many practical problems involve irregular Convex Domains, such as the human brain or heart, which are difficult to partition well with a structured mesh, the existing finite element method using the structured mesh is less efficient. Research on the finite element method using a completely unstructured mesh on an irregular Domain is of great significance. In this paper, a novel unstructured mesh finite element method is developed for solving the time-space fractional wave equation on a two-dimensional irregular Convex Domain. The novel unstructured mesh Galerkin finite element method is used to discretize in space and the Crank-Nicolson scheme is used to discretize the Caputo time fractional derivative. The implementation of the unstructured mesh Crank-Nicolson Galerkin method (CNGM) is detailed and the stability and convergence of the numerical scheme are analysed. Numerical examples are presented to verify the theoretical analysis. To highlight the ability of the proposed unstructured mesh Galerkin finite element method, a comparison of the unstructured mesh with the structured mesh in the implementation of the numerical scheme is conducted. The proposed numerical method using an unstructured mesh is shown to be more effective and feasible for practical applications involving irregular Convex Domains.
Xue Yang - One of the best experts on this subject based on the ideXlab platform.
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systems of reflected stochastic pdes in a Convex Domain analytical approach
Journal of Differential Equations, 2021Co-Authors: Xue Yang, Jing ZhangAbstract:Abstract In this paper, we establish an existence and uniqueness result for the system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a Convex Domain in R K by analytical approach. The method is based on the approximation of the penalized systems of SPDEs.
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reflected backward stochastic partial differential equations in a Convex Domain
Stochastic Processes and their Applications, 2020Co-Authors: Xue Yang, Qi Zhang, Tusheng ZhangAbstract:Abstract This paper is concerned with the reflected backward stochastic partial differential equations, taking values in a Convex Domain in R k . The existence and uniqueness of solution are studied under both the super-parabolic and parabolic conditions. In the degenerate parabolic case the connection between reflected backward stochastic partial differential equations and reflected forward backward stochastic differential equations is established.
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reflected backward stochastic partial differential equations with jumps in a Convex Domain
Statistics & Probability Letters, 2019Co-Authors: Xue YangAbstract:Abstract This paper is concerned with a class of multi-dimensional reflected backward stochastic partial differential equations (BSPDE for short), taking values in a Convex Domain in R k , which are driven by an infinite dimensional Brownian motion and an independent compensated Poisson random measure. Existence and uniqueness of the solution to this class of reflected BSPDEs are proved. Penalization method plays an important role.
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systems of reflected stochastic pdes in a Convex Domain analytical approach
arXiv: Probability, 2018Co-Authors: Xue Yang, Jing ZhangAbstract:In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a Convex Domain in R^k by analytical approach. The method is based on the approximation of the penalized systems of SPDEs.
Xiaoyun Jiang - One of the best experts on this subject based on the ideXlab platform.
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the unstructured mesh finite element method for the two dimensional multi term time space fractional diffusion wave equation on an irregular Convex Domain
Journal of Scientific Computing, 2018Co-Authors: Wenping Fan, Xiaoyun Jiang, Fawang Liu, Vo AnhAbstract:In this paper, the two-dimensional multi-term time-space fractional diffusion-wave equation on an irregular Convex Domain is considered as a much more general case for wider applications in fluid mechanics. A novel unstructured mesh finite element method is proposed for the considered equation. In most existing works, the finite element method is applied on regular Domains using uniform meshes. The case of irregular Convex Domains, which would require subdivision using unstructured meshes, is mostly still open. Furthermore, the orders of the multi-term time-fractional derivatives have been considered to belong to (0, 1] or (1, 2] separately in existing models. In this paper, we consider two-dimensional multi-term time-space fractional diffusion-wave equations with the time fractional orders belonging to the whole interval (0, 2) on an irregular Convex Domain. We propose to use a mixed difference scheme in time and an unstructured mesh finite element method in space. Detailed implementation and the stability and convergence analyses of the proposed numerical scheme are given. Numerical examples are conducted to evaluate the theoretical analysis.
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a novel unstructured mesh finite element method for solving the time space fractional wave equation on a two dimensional irregular Convex Domain
Fractional Calculus and Applied Analysis, 2017Co-Authors: Xiaoyun Jiang, Ian TurnerAbstract:Most existing research on applying the finite element method to discretize space fractional operators is studied on regular Domains using either uniform structured triangular meshes, or quadrilateral meshes. Since many practical problems involve irregular Convex Domains, such as the human brain or heart, which are difficult to partition well with a structured mesh, the existing finite element method using the structured mesh is less efficient. Research on the finite element method using a completely unstructured mesh on an irregular Domain is of great significance. In this paper, a novel unstructured mesh finite element method is developed for solving the time-space fractional wave equation on a two-dimensional irregular Convex Domain. The novel unstructured mesh Galerkin finite element method is used to discretize in space and the Crank-Nicolson scheme is used to discretize the Caputo time fractional derivative. The implementation of the unstructured mesh Crank-Nicolson Galerkin method (CNGM) is detailed and the stability and convergence of the numerical scheme are analysed. Numerical examples are presented to verify the theoretical analysis. To highlight the ability of the proposed unstructured mesh Galerkin finite element method, a comparison of the unstructured mesh with the structured mesh in the implementation of the numerical scheme is conducted. The proposed numerical method using an unstructured mesh is shown to be more effective and feasible for practical applications involving irregular Convex Domains.
Tusheng Zhang - One of the best experts on this subject based on the ideXlab platform.
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reflected backward stochastic partial differential equations in a Convex Domain
Stochastic Processes and their Applications, 2020Co-Authors: Xue Yang, Qi Zhang, Tusheng ZhangAbstract:Abstract This paper is concerned with the reflected backward stochastic partial differential equations, taking values in a Convex Domain in R k . The existence and uniqueness of solution are studied under both the super-parabolic and parabolic conditions. In the degenerate parabolic case the connection between reflected backward stochastic partial differential equations and reflected forward backward stochastic differential equations is established.
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Backward doubly SDEs and semilinear stochastic PDEs in a Convex Domain
Stochastic Processes and their Applications, 2017Co-Authors: Anis Matoussi, Wissal Sabbagh, Tusheng ZhangAbstract:This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDSDEs) in a Convex Domain D without any regularity conditions on the boundary. Moreover, using a stochastic flow approach a probabilistic interpretation for a system of reflected SPDEs in a Domain is given via such RBDSDEs. The solution is expressed as a pair (u, ν) where u is a predictable continuous process which takes values in a Sobolev space and ν is a random regular measure. The bounded variation process K, the component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D. This bounded variation process determines the measure ν from a particular relation by using the inverse of the flow associated to the the diffusion operator.
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backward doubly sdes and semilinear stochastic pdes in a Convex Domain
Stochastic Processes and their Applications, 2017Co-Authors: Anis Matoussi, Wissal Sabbagh, Tusheng ZhangAbstract:Abstract This paper presents existence and uniqueness results for reflected backward doubly stochastic differential equations (in short RBDSDEs) in a Convex Domain D without any regularity conditions on the boundary. Moreover, using a stochastic flow approach a probabilistic interpretation for a system of reflected SPDEs in a Domain is given via such RBDSDEs. The solution is expressed as a pair ( u , ν ) where u is a predictable continuous process which takes values in a Sobolev space and ν is a random regular measure. The bounded variation process K , the component of the solution of the reflected BDSDE, controls the set when u reaches the boundary of D . This bounded variation process determines the measure ν from a particular relation by using the inverse of the flow associated to the diffusion operator.
Laurent Saloffcoste - One of the best experts on this subject based on the ideXlab platform.
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the dirichlet heat kernel in inner uniform Domains local results compact Domains and non symmetric forms
Journal of Functional Analysis, 2014Co-Authors: Janna Lierl, Laurent SaloffcosteAbstract:Abstract This paper provides sharp Dirichlet heat kernel estimates in inner uniform Domains, including bounded inner uniform Domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the results apply to the Dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable real coefficients in inner uniform Domains in R n . The results are applicable to any Convex Domain, to the complement of any Convex Domain, and to more exotic examples such as the interior and exterior of the snowflake.
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the dirichlet heat kernel in inner uniform Domains local results compact Domains and non symmetric forms
arXiv: Functional Analysis, 2012Co-Authors: Janna Lierl, Laurent SaloffcosteAbstract:This paper provides sharp Dirichlet heat kernel estimates in inner uniform Domains, including bounded inner uniform Domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the results apply to the Dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable coefficients in inner uniform Domains in $\mathbb R^n$. The results are applicable to any Convex Domain, to the complement of any Convex Domain, and to more exotic examples such as the interior and exterior of the snowflake.