Estimates of the distance to the exact solution of parabolic problems   based on local Poincar\'e type inequalities
  The goal of the paper is to derive two-sided bounds of the distance between the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions and any function in the admissible energy space. 
Svetlana Matculevich and Sergey Repin
math.FA cs.NA