Search

The Fourier pseudo-spectral method has been studied for a one- dimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of con- vergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present method are compared to those obtained by using the Chebyshev spectral collocation method. The numerical results show that the proposed method outperforms the conventional one in terms of accuracy and convergence rate. [ABSTRACT FROM AUTHOR]

In this paper we give a new proof of the -error estimate for the finite element approximation of the Laplace-Beltrami equation with an additional lower order term on a surface. While the proof available in the literature uses the method of perturbed bilinear forms from Schatz and Wahlbin, we adapt Scott's proof from an Euclidean setting to the surface case. Furthermore, in contrast to the literature we use an approximative Green's function on the surface instead of an exact Green's function which is obtained by lifting an Euclidean Green's function locally from the tangent plane to the surface. [ABSTRACT FROM AUTHOR]

We consider linear ill-posed problems in Hilbert spaces with a noisy right hand side and a given noise level. To solve non-self-adjoint problems by the (iterated) Tikhonov method, one effective rule for choosing the regularization parameter is the monotone error rule (Tautenhahn&Hämarik, Inverse Problems, 1999, 15, 1487-1505). In this paper we consider the solution of self-adjoint problems by the (iterated) Lavrentiev method and propose for parameter choice an analog of the monotone error rule. We prove under certain mild assumptions the quasi-optimality of the proposed rule guaranteeing convergence and order optimal error estimates. Numerical examples show for the proposed rule and its modifications much better performance than for the modified discrepancy principle. [ABSTRACT FROM AUTHOR]

An error estimate for the minimal error method for nonlinear ill-posed problems under general a Hölder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a Hölder-type source condition, we obtain an optimal order error estimate. We also consider the modified minimal error method with noisy data and provide an error estimate. [ABSTRACT FROM AUTHOR]

A method for joint measuring the power law exponent and the structure constant of atmospheric turbulence is proposed and examined. The measurements are equivalent to solve the simultaneous equations formed by the irradiance scintillation index and the angle-of-arrival fluctuations variance, where the measured parameters are regarded as the unknowns. The measured error analysis is also presented. Based on our proposed method, the measured results accord with the daily trend of atmospheric turbulence. [ABSTRACT FROM AUTHOR]

We present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions. [ABSTRACT FROM AUTHOR]

We prove quasi-optimality of an adaptive finite element algorithm for a model problem of optimal control including control constraints. The quasi-optimility expresses the fact that the decrease of error with respect to the number of mesh cells is optimal up to a constant. The considered algorithm is based on an adaptive marking strategy which compares a standard residual-type a posteriori error estimator with a data approximation term in each step of the algorithm in order to adapt the marking of cells. [ABSTRACT FROM AUTHOR]

We study an efficient finite element method for the NS-ω model, that uses van Cittert approximate deconvolution to improve accuracy and Scott-Vogelius elements to provide pointwise mass conservative solutions and remove the dependence of the (often large) Bernoulli pressure error on the velocity error. We provide a complete numerical analysis of the method, including well-posedness, unconditional stability, and optimal convergence. Additionally, an improved choice of filtering radius (versus the usual choice of the average mesh width) for the scheme is found, by identifying a connection with a scheme for the velocity-vorticity-helicity NSE formulation. Several numerical experiments are given that demonstrate the performance of the scheme, and the improvement offered by the new choice of the filtering radius. [ABSTRACT FROM AUTHOR]