Remarks on numerical integration of $L^1$ norm

抄録

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.