7,387 research outputs found
Functional a posteriori error estimates for time-periodic parabolic optimal control problems
This paper is devoted to the a posteriori error analysis of multiharmonic
finite element approximations to distributed optimal control problems with
time-periodic state equations of parabolic type. We derive a posteriori
estimates of functional type, which are easily computable and provide
guaranteed upper bounds for the state and co-state errors as well as for the
cost functional. These theoretical results are confirmed by several numerical
tests that show high efficiency of the a posteriori error bounds
Robust error estimates in weak norms for advection dominated transport problems with rough data
We consider mixing problems in the form of transient convection--diffusion
equations with a velocity vector field with multiscale character and rough
data. We assume that the velocity field has two scales, a coarse scale with
slow spatial variation, which is responsible for advective transport and a fine
scale with small amplitude that contributes to the mixing. For this problem we
consider the estimation of filtered error quantities for solutions computed
using a finite element method with symmetric stabilization. A posteriori error
estimates and a priori error estimates are derived using the multiscale
decomposition of the advective velocity to improve stability. All estimates are
independent both of the P\'eclet number and of the regularity of the exact
solution
- …