On the optimal error bound for cubature formulae on certain classes of continuous functions

1977 ◽  
Vol 3 (1) ◽  
pp. 3-9 ◽  
Author(s):  
V. F. Babenko
Keyword(s):  
Error Bound ◽  
Continuous Functions ◽  
Optimal Error ◽  
Optimal Error Bound ◽  
Cubature Formulae

On the Recovery of Continuous Functions from Noisy Fourier Coefficients

2011 ◽  
Vol 11 (1) ◽  
pp. 75-82 ◽  
Author(s):  
Kosnazar Sharipov
Keyword(s):  
Error Bound ◽  
Fourier Coefficients ◽  
Regularization Parameter ◽  
A Priori ◽  
Continuous Functions ◽  
A Posteriori ◽  
Parameter Choice ◽  
Optimal Error ◽  
Ill Posed ◽  
Optimal Error Bound

AbstractWe consider the classical ill-posed problem of the recovery of continuous functions from noisy Fourier coefficients. For the classes of functions given in terms of generalized smoothness, we present a priori and a posteriori regularization parameter choice realizing an order-optimal error bound.

OPTIMAL ERROR BOUND AND APPROXIMATION METHODS FOR A CAUCHY PROBLEM OF THE MODIFIED HELMHOLTZ EQUATION

2011 ◽  
Vol 09 (02) ◽  
pp. 305-315 ◽  
Author(s):  
AILIN QIAN ◽  
YUJIANG WU
Keyword(s):  
Cauchy Problem ◽  
Helmholtz Equation ◽  
Error Estimates ◽  
Error Bound ◽  
Optimality Theory ◽  
Tikhonov Regularization Method ◽  
Regularization Methods ◽  
Optimal Error ◽  
Modified Helmholtz Equation ◽  
Optimal Error Bound

We consider a Cauchy problem for a modified Helmholtz equation, especially when we give the optimal error bound for this problem. Some spectral regularization methods and a revised Tikhonov regularization method are used to stabilize the problem from the viewpoint of general regularization theory. Hölder-type stability error estimates are provided for these regularization methods. According to the optimality theory of regularization, the error estimates are order optimal.

scholarly journals An embedded discontinuous Galerkin method for the Oseen equations

2021 ◽  
Author(s):  
Yongbin Han ◽  
Yanren Hou
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Error Bound ◽  
Discontinuous Galerkin Method ◽  
Convergence Order ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Oseen Equations ◽  
Optimal Error Bound ◽  
Convection Dominated

In this paper, the a prior error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the L 2 (Ω) norm, has an optimal error bound with convergence order k + 1, where the constants are dependent on the Reynolds number (or ν − 1 ), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order k +1 / 2. Here, k is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.

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