Remarks on numerical integration of $L^1$ norm

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Author(s)

Abstract

Non-differentiability of the absolute value function at the origin can affect the accuracy of numerical computations for the $L^1$ norm. We present an example in which the accuracy does deteriorate, and we provide a convergence order for such situations. We propose a simple algorithm to improve the convergence order, confirming its effectiveness as in the example described above. Mesh-dependent integrands and applications to finite element method are also considered.

Journal

  • JSIAM Letters

    JSIAM Letters 5(0), 5-8, 2013

    The Japan Society for Industrial and Applied Mathematics

Codes

  • NII Article ID (NAID)
    130003371111
  • Text Lang
    ENG
  • ISSN
    1883-0609
  • Data Source
    J-STAGE 
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