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Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
High order methods Discontinuous Galerkin Energy stability
2015/7/3
The purpose of this paper is to provide new insights on the connections that exist between the discontinuous Galerkin method (DG), the flux reconstruction method (FR) and the recently identi@...
Efficient Algorithms for High-Order Discretizations of the Euler and Navier-Stokes Equations
Efficient Algorithms High-Order Discretizations Euler Navier-Stokes Equations
2015/7/2
Higher order discretizations have not been widely successful in industrial applications to compressible ow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-...
Standard nearest-neighbour discretizations of Klein–Gordon models cannot preserve both energy and linear momentum
Discrete nonlinear klein GeDengBo equation the standard discrete linear momentum
2014/12/25
We consider nonlinear Klein–Gordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbours) may preserve either standardly defined linear momentum or standard...
Comparative study of different discretizations of the phi(4) model
The same discrete solitary wave spectral characteristics and functions
2014/12/25
We examine various recently proposed translationally invariant discretizations of the well-known ϕ4 field theory. We compare and contrast the properties of their fundamental solutions including t...
On a class of spatial discretizations of equations of the nonlinear Schrödinger type
Discrete nonlinear schrodinger equation nonlinear discrete model and discrete
2014/12/25
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a ...
Integrable semi-discretizations and full-discretization of the two dimensional Leznov lattice
Integrable system Integrable discretization cklund transformation Lax pair
2012/8/8
In this paper, semi-discretizations and full-discretization of the Leznov lattice are investigated via
Hirota's bilinear formalism. As a result, two integrable semi-discrete versions and one fully di...
Accuracy of Classical Conservation Laws for Hamilton PDES Under Runge-Kutta Discretizations
Accuracy of Classical Conservation Laws Hamilton PDES Runge-Kutta Discretizations
2012/8/7
We investigate conservative properties of Runge-Kutta methods
for Hamiltonian PDEs. It is shown that multi-symplecitic Runge-Kutta meth-
ods preserve precisely norm square conservation law. Based on...
Strong-Stability-Preserving, K-Step, 5- to 10-Stage, Hermite-Birkhoff Time-Discretizations of Order 12
Strong Stability Preserving, Hermite-Birkhoff Method SSP Coefficient Time Discretization Method of Lines Comparison with Other SSP Methods
2013/1/30
We construct optimal k-step, 5- to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of ord...
Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
Bä cklund Transformations trigonometric Gaudin model integrable time-discretizations
2010/4/2
We construct a two-parameter family of B\"acklund transformations for the trigonometric classical Gaudin magnet. The approach follows closely the one introduced by E.Sklyanin and V.Kuznetsov (1998,199...
Integrable discretizations for the short wave model of the Camassa-Holm equation
Integrable discretizations short wave Camassa-Holm equation
2010/4/2
The link between the short wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice (2DTL) is clarified. The parametric form of N-cuspon solution of th...
Integrable discretizations of the short pulse equation
Integrable discretizations short pulse equation
2010/4/6
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of s...
Another Reason Why Simple Discretizations of Rotated Diffusion Operators Cause Problems in Ocean Models: Comments on “Isoneutral Diffusion in a z-Coordinate Ocean Model”
Isoneutral Diffusion z-Coordinate Ocean Model Rotated Diffusion
2008/10/27
In recent papers (Griffies et al. 1998; Griffies 1998), the problem of isopycnal diffusion and Gent–McWilliams stirring in z-coordinate models was reviewed and a new discretization proposed. It was sh...
Asymptotic Behavior for Discretizations of a Semilinear Parabolic Equation with a Nonlinear Boundary Condition
Semidiscretizations Semilinear parabolic equation Asymptotic behavior Convergence
2010/1/22
This paper concerns the study of the numerical approximation for the following initial-boundary value problem: (P) where , and . We show that the solution of a semidiscrete form of (P) goes to ...
Some two-scale finite element discretizations are introduced for a
class of linear partial differential equations. Both boundary value
and eigenvalue problems are studied. Based on the two-scale err...
Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations
Attractor dissipative Zakharov equation
2007/12/10
In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist at...