Results 11 to 20 of about 16,319,430 (163)
A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations [PDF]
, 2007 In this paper we consider the numerical solution of first-order Hamilton-Jacobi equations using the combination of a discontinuous Galerkin finite element method and an adaptive $r$-refinement (mesh movement) strategy.
MacKenzie, John, Nicola, Aurelian
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Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System [PDF]
Communications on Applied Mathematics and Computation, 2021 Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, BBM-BBM system, Bona-Smith system etc.
Jiawei Sun, Shusen Xie, Yulong Xing
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Local Discontinuous Galerkin Methods for the Stokes System [PDF]
SIAM Journal on Numerical Analysis, 2002 A discontinuous Galerkin method for the Stokes problem is introduced and analysed. A priori error estimates for velocity and pressure are derived, which are shown to be optimal, if proper polynomial approximations and stabilization parameters are used.
Bernardo Cockburn +3 more
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An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type [PDF]
, 2011 We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time.
Brunner, Hermann +3 more
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The local discontinuous Galerkin method for the Oseen equations [PDF]
Mathematics of Computation, 2003 We introduce and analyze the local discontinuous Galerkin method for the Oseen equations of incompressible fluid flow. For a class of shape-regular meshes with hanging nodes, we derive optimal a priori estimates for the errors in the velocity and the pressure in
Bernardo Cockburn +2 more
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On the Local Discontinuous Galerkin Method for Linear Elasticity [PDF]
Mathematical Problems in Engineering, 2010 Following Castillo et al. (2000) and Cockburn (2003), a general framework of constructing discontinuous Galerkin (DG) methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear
Chen, Yuncheng +3 more
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A local discontinuous Galerkin method for the Burgers–Poisson equation [PDF]
Numerische Mathematik, 2014 The authors design, analyze and test a local discontinuous Galerkin method for solving the Burgers-Poisson equation. The proposed numerical method is high order accurate and preserves both momentum and energy invariants. The \(L^2\)-stability of the scheme for general solutions is a consequence of the energy preserving property.
Hailiang Liu, Nattapol Ploymaklam
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Comparison of high-order methods on unstructured grids [PDF]
, 2013 A high-order Discontinuous Galerkin (DG) method is formulated and implemented on the Cranfield University’s 3D unstructured Finite Volume Method (FVM) code (UCNS3D), for both linear and non-linear hyperbolic conservation laws and for test-cases which ...
Iqbal, Kashif H.
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A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods [PDF]
, 2008 We present here a domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method.
Dolean Maini, Victorita +2 more
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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
Deng, Weihua, Hesthaven, Jan S.
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