Error estimates in effective versions of Tchebotarev density theorem.

Akman, Füsun


Error estimates for space-time discontinuous Galerkin formulation based on proper orthogonal decomposition
Akman, Tuğba (Informa UK Limited, 2017-01-01)
In this study, proper orthogonal decomposition (POD) method is applied to diffusion-convection-reaction equation, which is discretized using spacetime discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and spacetime projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence ra...
Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization
Hacat, Gülnur; Yılmaz, Fikriye Nuray; Çıbık, Aytekin Bayram; Kaya Merdan, Songül (2022-10-01)
© 2022 Elsevier Inc.This paper presents a family of implicit-explicit (IMEX) time stepping scheme for the optimal control problem of the unsteady Navier-Stokes equations (NSE). The main feature of this kind of optimal control problem is that stabilization terms are proportional to discrete curvature of the solutions. First and second order optimality conditions are used for optimality of the curvature based stabilized Navier-Stokes equations. Complete stability and error analyses of state, adjoint and contr...
Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem
Koc, S; Song, JM; Chew, WC (Society for Industrial & Applied Mathematics (SIAM), 1999-04-29)
The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but fast-methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtain...
Error bound and simulation algorithm for piecewise deterministic approximations of stochastic reaction systems
Ganguly, Arnab; ALTINTAN, DERYA; Koeppl, Heinz (2015-07-03)
In cellular reaction systems, events often happen at different time and abundance scales. It is possible to simulate such multi-scale processes with exact stochastic simulation algorithms, but the computational cost of these algorithms is prohibitive due to the presence of high propensity reactions. This observation motivates the development of hybrid models and simulation algorithms that combine deterministic and stochastic representation of biochemical systems. Based on the random time change model we pro...
Error prediction in electromagnetic simulations using machine learning
KARAOSMANOGLU, BARISCAN; Ergül, Özgür Salih (2019-07-01)
© 2019 IEEE.We present a novel approach of using deep convolutional neural networks (CNN) to predict electromagnetic scattering errors in iterative solutions of electrically large three-dimensional objects. Deep CNN models are constructed and trained by using surface current images to predict far-zone scattering errors. Numerical experiments demonstrate successful predictions with more than 95% accuracy. The constructed models can be useful to quickly assess the accuracy of candidate solutions of current di...
Citation Formats
F. Akman, “Error estimates in effective versions of Tchebotarev density theorem.,” Middle East Technical University, 1986.