Remarks on numerical integration of $L^1$ norm

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概要

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• 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.

著者

• Kashiwabara Takahito

  Graduate School of Mathematical Sciences, The University of Tokyo

• Oikawa Issei

  Graduate School of Mathematical Sciences, The University of Tokyo

関連論文

• Remarks on numerical integration of $L^1$ norm
• Discontinuous Galerkin FEM of hybrid type
• Hybridized discontinuous Galerkin method with lifting operator

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