Local discontinuous Galerkin methods for fractional ordinary differential equations [PDF]
, 2014 This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs).
Deng, Weihua, Hesthaven, Jan S.
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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 +3 more
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Using a LDG method for solving an inverse source problem of the time-fractional diffusion equation [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2017 In this paper, we apply a local discontinuous Galerkin (LDG) method to solve some fractional inverse problems. In fact, we determine a timedependent source term in an inverse problem of the time-fractional diffusion equation.
Somayeh Yeganeh +2 more
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Pointwise best approximation results for Galerkin finite element solutions of parabolic problems [PDF]
, 2016 In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm.
Leykekhman, Dmitriy, Vexler, Boris
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Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws
Mathematics, 2021 This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws.
Ernesto Guerrero Fernández +2 more
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Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond [PDF]
Geoscientific Model Development, 2020 Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows.
T. H. Gibson +3 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
W.H. Deng, J.S. Hesthaven
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Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity [PDF]
, 2019 Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the ...
Giacomini, Matteo +1 more
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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 +3 more
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