A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers

0342835 - ÚI 2011 RIV US eng J - Journal Article
Jiránek, P. - Strakoš, Zdeněk - Vohralík, M.
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers.
SIAM Journal on Scientific Computing. Roč. 32, č. 3 (2010), s. 1567-1590. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA AV ČR IAA100300802
Grant - others:GA ČR(CZ) GP201/09/P464
Institutional research plan: CEZ:AV0Z10300504
Keywords : second-order elliptic partial differential equation * finite volume method * a posteriori error estimates * iterative methods for linear algebraic systems * conjugate gradient method * stopping criteria
Subject RIV: BA - General Mathematics
Impact factor: 3.016, year: 2010

For the finite volume discretization of a second-order elliptic model problem, we derive a posteriori error estimates which take into account an inexact solution of the associated linear algebraic system. We show that the algebraic error can be bounded by constructing an equilibrated Raviart-Thomas-Nédélec discrete vector field whose divergence is given by a proper weighting of the residual vector. Next, claiming that the discretization error and the algebraic one should be in balance, we construct stopping criteria for iterative algebraic solvers.Using this convenient balance, we also prove the efficiency of our a posteriori estimates; i.e., we show that they also represent a lower bound, up to a generic constant, for the overall energy error. A local version of this result is also stated. This makes our approach suitable for adaptive mesh refinement which also takes into account the algebraic error.
Permanent Link: http://hdl.handle.net/11104/0185458