Mitsuhiro T. Nakao, Nobito Yamamoto and Yoshitaka Watanabe:
Guaranteed Error Bounds for the Finite Element Solutions of the Stokes Problem,
Scientific Computing and Validated Numerics, Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95, held in Wuppertal, Germany, September 26-29, 1995 (G. Alefeld, A. Frommer, B. Lang, eds.), Mathematical Research, Volume 90, Akademie Verlag (1996) pp.258-264.

We describe a method to estimate the guaranteed accuracy of the finite element solutions for the Stokes problem. We show that an a posteriori error can be computed by using the numerical estimates of a constant related to the so called inf-sup condition for the continuous problem.

Also a method to derive the constructive a priori error estimates are considered.

Furthermore, we will mention about the numerical verification method of the solution for the stationary Navier-Stokes equation incorporating with these error estimates. 7pages.

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