Results 11 to 20 of about 523 (187)

Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain

Computation, 2020
In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva, Maria Vasilyeva, Eric T. Chung   +2 more
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An analytical and numerical approach for the $(1+1)$-dimensional nonlinear Kolmogorov–Petrovskii–Piskunov equation [PDF]

Iranian Journal of Numerical Analysis and Optimization
The main focus of this work is to develop and implement an efficient lo-cal discontinuous Galerkin scheme for acquiring the numerical solution of the (1 + 1)-dimensional nonlinear Kolmogorov–Petrovskii–Piskunov equa-tion. The proposed framework employs a
A. Chand, J. Mohapatra
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Local Discontinuous Galerkin methods for fractional diffusion equations [PDF]

ESAIM: Mathematical Modelling and Numerical Analysis, 2013
We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems in one space dimension, characterized by having fractional derivatives, parameterized by beta in [1,2]. After demonstrating that a classic approach fails to deliver optimal order of convergence, we introduce a modified local numerical flux
W.H. Deng, J.S. Hesthaven
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Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation

Mathematical Modelling and Analysis, 2012
In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation.
Zongxiu Ren, Leilei Wei, Yinnian He, Shaoli Wang   +3 more
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations

Advances in Mathematical Physics, 2017
We focus on developing the finite difference (i.e., backward Euler difference or second-order central difference)/local discontinuous Galerkin finite element mixed method to construct and analyze a kind of efficient, accurate, flexible, numerical schemes
Meilan Qiu, Liquan Mei, Dewang Li
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The local discontinuous Galerkin method for contaminant transport [PDF]

Advances in Water Resources, 2000
Abstract We develop a discontinuous finite element method for advection–diffusion equations arising in contaminant transport problems, based on the Local Discontinuous Galerkin (LDG) method of Cockburn B and Shu CW. (The local discontinuous Garlerkin method for time-dependent convection–diffusion systems. SIAM J Numer Anal 1998;35:2440–63).
Vadym Aizinger, Clint Dawson, Bernardo Cockburn, Paul Castillo   +3 more
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Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations

Journal of Inequalities and Applications, 2022
In this paper, we study the error estimates of local discontinuous Galerkin methods based on the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations.
Hui Bi, Yixin Chen
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Local Discontinuous Galerkin Method Coupled with Nonuniform Time Discretizations for Solving the Time-Fractional Allen-Cahn Equation

Fractal and Fractional, 2022
This paper aims to numerically study the time-fractional Allen-Cahn equation, where the time-fractional derivative is in the sense of Caputo with order α∈(0,1). Considering the weak singularity of the solution u(x,t) at the starting time, i.e., its first
Zhen Wang, Luhan Sun, Jianxiong Cao
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Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations [PDF]

Communications in Computational Physics, 2017
AbstractBy combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in ℝ2. The nonlinear stability is proved for the proposed symmetric variational formulation.
Wang, Shuqin, Deng, Weihua, Yuan, Jinyun, Wu, Yujiang   +3 more
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A Computational Study of an Implicit Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations

Abstract and Applied Analysis, 2014
We propose, analyze, and test a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and local discontinuous Galerkin methods ...
Leilei Wei, Xindong Zhang
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