Results 31 to 40 of about 19,690 (191)
Fractal and Fractional, 2022 In this paper, efficient methods seeking the numerical solution of a time-fractional fourth-order differential equation with Caputo’s derivative are derived. The solution of such a problem has a weak singularity near the initial time t=0. The Caputo time-
Zhen Wang
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Discrete Dynamics in Nature and Society, 2016 We present a new numerical method for solving nonlinear reaction-diffusion systems with cross-diffusion which are often taken as mathematical models for many applications in the biological, physical, and chemical sciences.
Na An +3 more
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Local discontinuous Galerkin method for phase transition problems [PDF]
, 2015 In this thesis we develop a local discontinuous Galerkin (LDG) finite element method to solve mathematical models for phase transitions in solids and fluids. The first model we study is called a viscosity-capillarity (VC) system associated with phase transitions in elastic bars and Van der Waals fluids.
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HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II. Optimization of the Runge-Kutta smoother [PDF]
, 2011 Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator.
Rhebergen, S., Vegt, J.J.W. van der
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Journal of Inequalities and Applications, 2017 In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is ( k + 3 / 2 ) $(k+3/2)$ th-order superconvergent to a particular projection ...
Hui Bi, Chengeng Qian
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Efficient time discretization for local discontinuous Galerkin methods
Discrete & Continuous Dynamical Systems - B, 2007 In this paper, we explore three efficient time discretization techniques for the local discontinuous Galerkin (LDG) methods to solve partial differential equations (PDEs) with higher order spatial derivatives. The main difficulty is the stiffness of the LDG spatial discretization operator, which would require a unreasonably small time step for an ...
Yinhua Xia, Yan Xu, Chi-Wang Shu
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An advection-robust Hybrid High-Order method for the Oseen problem [PDF]
, 2018 In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces, while the ...
Aghili, Joubine, Di Pietro, Daniele A.
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A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations
East Asian Journal on Applied Mathematics, 2020 Summary: A local discontinuous Galerkin finite element method for a class of timefractional Burgers equations is developed. In order to achieve a high order accuracy, the time-fractional Burgers equation is transformed into a first order system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space.
Yuan, Wenping +2 more
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Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes [PDF]
, 2016 We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include ...
Boscheri, Walter, Dumbser, Michael
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Numerical modeling of seismic waves by discontinuous spectral element methods★
ESAIM: Proceedings and Surveys, 2018 We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes.
Antonietti Paola F. +6 more
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