A posteriori error estimates and adaptive methods for incompressible viscous flow problems
This thesis is focused on the development and numerical justification of a modern computational methodology that provides guaranteed upper bounds of the energy norms of an error. The methodology suggested is based on the so-called functional type a posteriori error estimates. Different linearizations of the Navier-Stokes equations are considered. Namely, estimates of the Stokes problem, the evolutionary Stokes problem and the system with rotation are proposed. For the system with rotation and semi-discrete approximations of the evolutionary Stokes problem, such type of estimates are presented for the first time. For the Stokes problem and the system with rotation, different numerical strategies are implemented. Numerical tests are performed in Cartesian and Cylindrical coordinate system. For the Stokes problem, a posteriori error estimates on a certain subdomain of interest are also tested. It is shown that functional type a posteriori error estimation methods give reliable and robust upper bounds of the error and realistic error indication. The approach suggested allows to construct efficient mesh-adaptive algorithms and provide a guaranteed accuracy for the approximate solutions. ...
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- Väitöskirjat 
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Nokka, Marjaana (University of Jyväskylä, 2016)The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham ...
On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm Anjam, Immanuel; Nokka, Marjaana; Repin, Sergey (De Gruyter, 2012)In this paper, we derive computable a posteriori error bounds for approximations computed by the Uzawa algorithm for the generalized Stokes problem. We show that for each Uzawa iteration both the velocity error and the ...
Pauly, D.; Repin, S. (American Mathematical Society, 2019)This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains and applications to the derivation of computable bounds for the distance between the exact ...
Anjam, Immanuel; Pauly, Dirk (University of Jyväskylä, 2014)
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems Matculevich, Svetlana; Wolfmayr, Monika (Elsevier, 2018)This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker–Planck problem appearing in computational neuroscience. ...