Počet záznamů: 1

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

  1. 1.
    0342835 - UIVT-O 2011 RIV US eng J - Článek v odborném periodiku
    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
    Grant CEP: GA AV ČR IAA100300802
    Grant ostatní: GA ČR(CZ) GP201/09/P464
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: second-order elliptic partial differential equation * finite volume method * a posteriori error estimates * iterative methods for linear algebraic systems * conjugate gradient method * stopping criteria
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 3.016, rok: 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.
    Trvalý link: http://hdl.handle.net/11104/0185458