A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (Lead / Corresponding author)

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    We prove a posteriori error estimates of optimal order for linear Schrodinger-type equations in the L8(L(2)- and the L8(H1)-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis et al. in [Math. Comput. 75 (2006) 511-531], leads to a posteriori upper bounds that are of optimal order in the L8(L2)-norm, but of suboptimal order in the L8(H(1)-norm. The optimality in the case of L8(H(1))-norm is recovered by using an auxiliary initial-and boundary-value problem.

    Original languageEnglish
    Pages (from-to)761-778
    Number of pages18
    JournalEsaim: Mathematical Modelling and Numerical Analysis
    Volume45
    Issue number4
    Early online date21 Feb 2011
    DOIs
    Publication statusPublished - Jul 2011

    Keywords

    • TIME
    • energy techniques
    • GALERKIN METHOD
    • a posteriori error analysis
    • Crank-Nicolson method
    • Linear Schrodinger equation
    • FINITE-ELEMENT-METHOD
    • L(infinity)(L(2))- and L(infinity)(H(1))-norm
    • Crank-Nicolson reconstruction

    Cite this