Sentence examples for maximum norm errors from inspiring English sources

We will measure the accuracy of the proposed scheme using the maximum norm errors defined by e^{n}_{epsilon}=bigl| v^{n}-u^{n}bigr| _{infty}.

The maximum norm errors between the exact and the numerical solutions are denoted by E_{infty}(h,tau)=max_{1leq nleq N} biglVert u^{n}-U^{n} bigrVert _{infty}.

In the test, we compute the maximum norm errors between the exact and the numerical solutions at the last time step by e(h,tau)=max_{1leq ileq N} biglvert u(x_{i},t_{M} -u_{i}^{M} -u_{i}rt, (11) where (u(x_{i},t_{M})) is the exact solution and (u_{i}^{M}) is the numerical solution with the mesh step sizes h and τ at the grid point ((x_{i},t_{M})).

For results on maximum norm error analysis of overlapping nonmatching grids methods for elliptic problems we refer, for example, to [9 14].

Quite a few works on maximum norm error analysis of overlapping nonmatching grids methods for elliptic problems are known in the literature (cf., e.g., [11 14]).

Zhang et al. [22] presented a Crank-Nicolson-type difference scheme for a subdiffusion equation with Riemann-Liouville fractional derivative, where the discrete (H_{1}) norm convergence was proved rigorously, and the maximum norm error estimate was given.

These figures show that the maximum norm error, defined in Eq. (11), becomes relatively smaller as the mesh size becomes smaller, which provides the validation of our results once again.

Fixing the spatial step (h=1/1text000) and taking different temporal steps, Table 1 presents the maximum (L_{2}) norm errors and convergence orders of our schemes; fixing the temporal step (tau =1/10text000) and taking different spatial steps, Table 2 presents the (L_{2}) norm errors and convergence orders in spatial direction.

An upper bound of the Hausdorff distance between planar curve and conic section can be expressed by the maximum norm of error function from the conic section to the planar curve (Comput. Aided Geomet. Design, 14 (1997) 135 151).

Refinement in spatial and angular discretization was investigated and the calculation accuracy is studied via the difference of the multiplication factor from reference value and via the root-mean-square and maximum norm of the error in the pin power.

We develop a family of functionals Ir u), with the property that the maximum norm of the error is bounded by Ir u /Jr, where r is an integer and J is the degree of the polynomial approximation.