نتایج جستجو برای: order of accuracy

تعداد نتایج: 21203890  

Journal: :Math. Comput. 2007
Todd F. Dupont Yingjie Liu

Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method developed in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved o...

2016
EVAN S. GAWLIK MELVIN LEOK

We study schemes for interpolating functions that take values in the special orthogonal group SO(n). Our focus is on interpolation schemes obtained by embedding SO(n) in a linear space, interpolating in the linear space, and mapping the result onto SO(n) via the closest point projection. The resulting interpolants inherit both the order of accuracy and the regularity of the underlying interpola...

Journal: :J. Comput. Physics 2011
Sofia Eriksson Qaisar Abbas Jan Nordström

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing SummationBy-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the...

2009
Yingjie Liu Chi-Wang Shu Zhiliang Xu

The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. However, there are still small remaining overshoots/undershoots in the vicinity of discontinuities. HR with partial neighboring cells [Xu, Liu and Shu, JCP ’09] essentially overcom...

Journal: :Math. Comput. 2006
M. Z. Liu Z. W. Yang Y. Xu

In the present paper, the modified Runge-Kutta method is constructed, and it is proved that the modified Runge-Kutta method preserves the order of accuracy of the original one. The necessary and sufficient conditions under which the modified Runge-Kutta methods with the variable mesh are asymptotically stable are given. As a result, the θ-methods with 1 2 ≤ θ ≤ 1, the odd stage Gauss-Legendre m...

Journal: :SIAM J. Numerical Analysis 1999
Bengt Fornberg Michelle Ghrist

The simplest finite difference approximations for spatial derivatives are centered, explicit, and applied to “regular” equispaced grids. Well-established generalizations include the use of implicit (compact) approximations and staggered grids. We find here that the combination of these two concepts, together with high formal order of accuracy, is very effective for approximating the first deriv...

Journal: :J. Comput. Physics 2006
Emilie Marchandise Jean-François Remacle Nicolas Chevaugeon

A quadrature free, Runge–Kutta discontinuous Galerkin method (QF-RK-DGM) is developed to solve the level set equation written in a conservative form on twoand tri-dimensional unstructured grids. We show that the DGM implementation of the level set approach brings a lot of additional benefits as compared to traditional ENO level set realizations. Some examples of computations are provided that d...

Journal: :SIAM J. Numerical Analysis 2001
Peter Mathé Sergei V. Pereverzyev

We study the efficiency of the approximate solution of ill-posed problems, based on discretized noisy observations, which we assume to be given beforehand. A basic purpose of the paper is the consideration of stochastic noise, but deterministic noise is also briefly discussed. We restrict ourselves to problems which can be formulated in Hilbert scales. Within this framework we shall quantify th...

1998
Mark H. Carpenter Jan Nordstrom David Gottlieb MARK H. CARPENTER DAVID GOTTLIEB

Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operato...

Journal: :SIAM J. Numerical Analysis 2011
David I. Ketcheson Sigal Gottlieb Colin B. Macdonald

We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TS...

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