Combined error estimates in the case of dimension reduction

Abstract

We consider the stationary reaction-diffusion problem in a domain Ω⊂ℝ 3 $\Omega \subset \mathbb {R}^3$ having the size along one coordinate direction essentially smaller than along the others. By an energy type argumentation, different simplified models of lower dimension can be deduced and solved numerically. For these models, we derive a guaranteed upper bound of the difference between the exact solution of the original problem and a three-dimensional reconstruction generated by the solution of a dimensionally reduced problem. This Show more