In this paper, we establish sharp error estimates of residual type for nite element approximation to elliptic obstacle problems. The estimates are of mixed nature, which are neither of a pure a priori form nor of a pure a posteriori form but instead they are combined by an a priori part and an a posteriori part. The key ingredient in our derivation for the mixed error estimates is the use of a ...

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research the Institute Computer Science, Czestochowa University Technology

This paper is concerned with a posteriori error bounds for wide class of numerical schemes, $$n\times n$$ hyperbolic conservation laws in one space dimension. These estimates are achieved by “post-processing algorithm”, checking that the solution retains small total variation, and computing its oscillation on suitable subdomains. The results apply, particular, to solutions obtained Godunov or L...