[PDF] Top 20 Error estimate for finite element methods for scalar conservation laws

... More precisely, we obtain new a posteriori error estimates which are then used to prove that the SCSD method and the SCDG method converge to the entropy solution of (1.1), (1.2) in the L[r] ... See full document

... The error estimate presented in this paper is the first a priori error estimate and the first optimal error estimate for numerical schemes for scalar conservation ... See full document

... priori error estimates for scalar conservation laws, based on the original Kuznetsov approximation theory ...global error of these schemes seems to be insensitive to the deterioration ... See full document

... for scalar conservation laws have attracted attention for the last few ...as error estimates have not been totally ...the error bound for the following Cauchy problem of conser- vation ... See full document

... priori error estimates for numerical methods for scalar conservation laws was ...priori error estimates for the Engquist- Osher scheme [9] on one-dimensional uniform grids; in ... See full document

... and error estimation for stochastic fractional ...numerical methods for these kinds of frac- tional SPDEs are rarely studied, and we only note ...the error estimation of nonlinear fractional ... See full document

... Supraconvergence of numerical schemes has been analyzed in a variety of cases. For example, Manteuffel and White [17] studied supraconvergence for linear, second- order boundary value problems, Kreiss et al. [11] for ... See full document

... finite element method for fractional stochastic Navier–Stokes equations driven by white ...finite element method and the time discretization is obtained by the backward Euler ... See full document

... posteriori error estimates of the mixed finite element method for the optimal control problems governed by fourth order hyperbolic ...posteriori error estimates for both the state and the control ... See full document

... decades, finite element methods (FEM) have been developed to be one of the most popular and efficient methods not only for partial differential equations [26], but also for many scientific ... See full document

... Optimal error estimates for the approximate solution, its expectation and a Monte-Carlo approximation are contained in Section ...optimal error estimates extend to corresponding fully discrete ... See full document

... a finite elements mesh without any requirement on continuity between neighboring elements and can be considered a generalization of the finite volume and finite element methods ...of ... See full document

... Table 1 shows result of Equation (8) subject to initial condition (9). The obtained result shows that the Lax-Wendroff method produced errors slightly less than the other methods hence, more accurate. This shows ... See full document

... To conclude the discussion of this example, let us mention that the multi-dimensional analogue of the problem considered here has a different nature. In this case, a hyperbolic equation for the saturation u is coupled to ... See full document

... Inspired by the results of [4] in probability theory, the gradient flow structure of (3) led to several results on the large time asymptotic behaviour of solutions. A first result by Toscani [55] on the heat equation was ... See full document

... Abstract Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of parti- cles can be modeled by a nonlinear first order ... See full document

... scalar effective index method for large pitches. The disadvantages of empirical relations method appears for small air filling fractions and small pitches, when it does not answer for all range of wavelengths. After ... See full document

... homogenization methods, as we will show in this paper, FEM with numerical integration cannot be avoided as by its nature the macroscopic solver can only be defined at quadrature ...quantitative error bounds ... See full document

... finite element method for integro-differential equations using any degree of ...the error between the approximate solution and the Ritz-Volterra projection of the exact ... See full document

... classical methods for solving hyperbolic systems of conservation laws: the struc- tured Finite Volume method (FV), the high order Discontinuous Galerkin (DG) method and the Particle-In-Cell ... See full document