A posteriori error identities for the evolutionary Stokes problem

S. Repin

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 261-285

Résumé

This paper is concerned with functional identities that control distances between the exact solution of the evolutionary Stokes problem and a function from the corresponding energy space. Left hand sides of the identities contain norms of errors associated with velocity and stress fields error and the right hand ones contain known data and integrals that can be either directly computed or estimated via known quantities. It is shown that identities yield guaranteed and fully computable bounds of errors. A posteriori error identities and estimates are derived in the most general form. They do not use Galerkin orthogonality, divergence free property, or other special features of functions compared with the exact solution. Therefore, they are applicable for a wide variety of approximations, regardless of the method by which they were obtained.

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