Počet záznamů: 1  

Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations

  1. 1.
    0428023 - UIVT-O 2015 RIV US eng J - Článek v odborném periodiku
    Papež, Jan - Liesen, J. - Strakoš, Z.
    Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations.
    Linear Algebra and Its Applications. Roč. 449, 15 May (2014), s. 89-114. ISSN 0024-3795
    Grant CEP: GA AV ČR IAA100300802; GA ČR GA201/09/0917
    Grant ostatní:GA MŠk(CZ) LL1202; GA UK(CZ) 695612
    Institucionální podpora: RVO:67985807
    Klíčová slova: numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebraic error * spatial distribution of the error
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.939, rok: 2014

    In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary value model problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is not restricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere.
    Trvalý link: http://hdl.handle.net/11104/0233442