A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems
Provides rigorous error bounds for nonconforming approximations in convection-diffusion problems, but the approach is incremental and extends existing a posteriori estimation techniques.
The paper derives computable upper bounds for the error between exact and approximate solutions of evolutionary convection-diffusion problems, using integral identity transformations. The estimates are independent of the exact solution and involve only global constants from embedding inequalities.
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral identity that defines the generalized solution. These estimates depend on neither special properties of the exact solution nor its approximation, and involve only global constants coming from embedding inequalities. The estimates are first derived for functions in the corresponding energy space, and then possible extensions to classes of piecewise continuous approximations are discussed.