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2005 Richard Tapia Celebration of Diversity in Computing Conference
We present a numerical study for two systems of conservation laws using a spacetime discontinuous Galerkin (SDG) method with causal spacetime triangulations and the piecewise constant Galerkin basis. ... The SDG method is consistent with the weak formulation of conservation laws, and, in the case of strictly hyperbolic systems, also with the Lax entropy condition. ... However, the numerical experiments presented in this paper show that the SDG method can be successfully used in approximating solutions to more general systems of conservation laws. ...doi:10.1109/rtcdc.2005.201639 fatcat:ka2xnakb5jeijhqbgusrjcmmbq
We present a numerical study for two systems of conservation laws using a spacetime discontinuous Galerkin (SDG) method with causal spacetime triangulations and the piecewise constant Galerkin basis. ... The SDG method is consistent with the weak formulation of conservation laws, and, in the case of strictly hyperbolic systems, also with the Lax entropy condition. ... However, the numerical experiments presented in this paper show that the SDG method can be successfully used in approximating solutions to more general systems of conservation laws. ...doi:10.1145/1095242.1095256 dblp:conf/tapia/Jegdic05 fatcat:y66vfiajgfa4zgcvy2g2m2sprm
Sherwin, A high order Fou- rier/unstructured discontinuous Galerkin method for hyperbolic conservation laws (875-884); Armen Shirikyan and Leonid Vole- vich, Asymptotic properties of solutions to high-order ... Galkin, Global correctness of Cauchy problem for nonlinear conservation laws systems and one example for the gas dynamics (361-367); Isabelle Gallagher, Asymptotics for hyper- bolic equations with a skew-symmetric ...
Acknowledgments 32 References 32 On the Galerkin method for the Serre equations Comparing the cB and Serre systems, Eqs. (1.3a) and (1.1a) are the same. ... For this reason, the Serre system is often called fully-nonlinear shallow-water equations. ... No stability or convergence results are known for the nonlinear (semi-or fully-) discrete schemes for the Serre equations. ...doi:10.1007/s10915-014-9823-3 fatcat:u65etoxm4vbx7nqhapdallj3iy
A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. ... The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an explicit fourth-order Runge-Kutta method in time. ... No stability or convergence results are known for the nonlinear (semi-or fully-) discrete schemes for the Serre equations. ...arXiv:1306.3321v3 fatcat:6as6zaakffehflyfj34cteseg4
A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. ... After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions ... Acknowledgment The authors were supported by the Marsden Fund administered by the Royal Society of New Zealand. ...doi:10.1002/fld.4293 fatcat:7kj5tetjfnbh5i4lysbudhzlpi
In Part II the method is extended to finite element methods for scalar conservation laws in one space dimension. ... The quasimonotone method is a hybridization of a monotone method with a high order accurate method, designed to give stability near discontinuities as well as high order accuracy. ...
9 This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) 10 method to solve the fully nonlinear and weakly dispersive flows, within a scope to 11 simultaneously address accuracy ... In the context of numerically solving elliptic equations with higher order derivatives, 100 often the so-called Local Discontinuous Galerkin (LDG) method is employed as proposed in 101 Cockburn and Shu ... Acknowledgments 650 The authors are grateful for two anonymous reviewers for their insightful reviews, which ...doi:10.1016/j.ocemod.2018.03.006 fatcat:k4cb7myhavgxhidyvuhcisi2jm
Serre, Slow dynamics of linear waves in nonlinear systems of conservation laws (247-260). A. Jeffrey [Alan Jeffrey] and Y. G. ... Jie Shen and Roger Temam, Nonlinear Galerkin method using Legendre polynomials (363-376); Joel Smoller and Blake Temple, Multi-dimensional shock-waves for relativistic fluids (377-391); Hesheng Sun, Nonlinear ...
The ability of the Serre or Green Naghdi (S-GN) equations to reproduce this nonlinear processes is reviewed. ... Two high-order methods for solving S-GN equations, based on Finite Volume approaches, are presented. ... This work has also been supported by the ANR MathOcean, the ANR MISEEVA and the project ECOS-CONYCIT action C07U01. ...doi:10.1016/j.euromechflu.2011.02.005 fatcat:tiwjov6s5bhhvn5dacg7sii5ne
Lin, Characteristic Galerkin methods for hyperbolic prob- lems (430-439); Ingo Miiller and Wolf Weiss, The symmetric hy- perbolic equations of extended thermodynamics (440-448); Jean- Philippe Nicolas, ... Zhao [Yan Chun Zhao], A generalized Lagrangian method for solving the Euler equations (336-346). ...
We consider the hyperbolic reformulations of two different nonlinear dispersive systems, namely the Serre–Green–Naghdi model of dispersive water waves and the defocusing nonlinear Schrödinger equation. ... The first order hyperbolic reformulation of the Schrödinger equation is endowed with a curl involution constraint that needs to be properly accounted for in multiple space dimensions. ... Discontinuous Galerkin finite element schemes for the solution of nonlinear dispersive Boussinesq-type equations were forwarded in [50, 54, 55] . ...doi:10.1007/s10915-021-01429-8 fatcat:gmojrsmqljfndpb2nppqtnab2a
The governing partial differential equations are then solved at the aid of high order ADER discontinuous Galerkin finite element schemes. ... We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. ... for the Environment and Security (SIES). ...arXiv:2003.14309v1 fatcat:wjkehkqmxfdulk465adktdpmby
The reformulated Serre equations involve the water depth and a new quantity as the conserved variables which are evolved using the finite volume method. ... The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. ... Geological Survey for providing the rectangular wave data. ...arXiv:1607.08019v1 fatcat:hfgu2xg3s5habbjjmru5mwifxe
Pinder, Single- degree freedom collocation method using Hermite polynomials (489-499); Xijun Yu and Yonghong Wu, A Taylor-Galerkin finite element method for one-dimensional hyperbolic conservation laws ... Wheeler, Non conforming methods for transport with nonlinear reaction (421—432); Louis F. ...
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