Local a posteriori estimates for the Stokes problem
- 18 Downloads
We obtain computable estimates of the difference between an exact solution of the Stokes problem and an approximation from a respective energy class. The estimates are presented in terms of local norms and linear functionals. Certain generalizations to some nonlinear problems are discussed. Bibliography: 17 titles.
KeywordsExact Solution Nonlinear Problem Local Norm Linear Functional Stokes Problem
Unable to display preview. Download preview PDF.
- 1.M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis, Wiley (2000).Google Scholar
- 3.W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations, Birkhäuser, Berlin (2003).Google Scholar
- 4.M. Feistauer, Mathematical Methods in Fluid Dynamics, Longman, Harlow (1993).Google Scholar
- 6.M. Fuchs and G.A. Seregin, “Variational methods for problems from plasticity theory and for generalized Newtonian fluids,” Lect. Notes Math., 1749 (2000).Google Scholar
- 7.V. Girault and P. A. Raviart, “Finite element approximation of the Navier-Stokes equations,” Lect. Notes Math., 749 (1979).Google Scholar
- 8.O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York (1969).Google Scholar
- 9.O. A. Ladyzhenskaya, “On nonlinear problems of continuum mechanics,” Proc. Internat. Congr. Math. (Moscow 1966), Amer. Math. Soc. Transl. (2), 70 (1968).Google Scholar
- 15.S. Repin, S. Sauter, and A. Smolianski, “A posteriori error estimation for the Dirichlet problem with account of the error in approximation of boundary conditions,” Computing, No. 3, 147–168 (2003).Google Scholar