Equivalent Conditions for Local Error Bounds

2012 ◽  
Vol 20 (4) ◽  
pp. 617-636 ◽  
Author(s):  
K. W. Meng ◽  
X. Q. Yang
Keyword(s):  
Error Bounds ◽  
Local Error ◽  
Local Error Bounds ◽  
Equivalent Conditions

Local error bounds for static and stationary fields

2000 ◽  
Vol 36 (4) ◽  
pp. 1615-1618
Author(s):  
G. Rubinacci ◽  
R. Fresa ◽  
R. Albanese
Keyword(s):  
Error Bounds ◽  
Local Error ◽  
Local Error Bounds

scholarly journals Error Bound for Conic Inequality in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiangxing Zhu ◽  
Qinghai He ◽  
Jinchuan Lin
Keyword(s):  
Hilbert Space ◽  
Error Bound ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Local Error ◽  
Local Error Bound ◽  
Local Error Bounds ◽  
Space Case ◽  
Vector Valued Functions ◽  
Vector Valued

We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality. In the Hilbert space case, our result improves and extends some existing results on local error bounds.

Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hu Chen ◽  
Martin Stynes
Keyword(s):  
Diffusion Equation ◽  
Error Bounds ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Complete Monotonicity ◽  
Initial Time ◽  
Local Error ◽  
Time Fractional Diffusion Equation ◽  
Numer Anal

Abstract Time-fractional initial-boundary problems of parabolic type are considered. Previously, global error bounds for computed numerical solutions to such problems have been provided by Liao et al. (SIAM J. Numer. Anal. 2018, 2019) and Stynes et al. (SIAM J. Numer. Anal. 2017). In the present work we show how the concept of complete monotonicity can be combined with these older analyses to derive local error bounds (i.e., error bounds that are sharper than global bounds when one is not close to the initial time t = 0 {t=0} ). Furthermore, we show that the error analyses of the above papers are essentially the same – their key stability parameters, which seem superficially different from each other, become identical after a simple rescaling. Our new approach is used to bound the global and local errors in the numerical solution of a multi-term time-fractional diffusion equation, using the L1 scheme for the temporal discretisation of each fractional derivative. These error bounds are α-robust. Numerical results show they are sharp.

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