### Table 1: Features of dual composition discretizations of the KdV equation on the circle, using the function spaces Ftrig := trigonometric polynomials or Fpp(r) := Cr piecewise polynomials (of suitable degree).

"... In PAGE 30: ... However, the discretization, this time, is not Hamiltonian. Table1... ..."

### Table 1. Maximum errors je j1 for Example 3.8 using the - rules and Radau quadrature on uniform N-element meshes with piecewise polynomials of uniform degree p.

1998

"... In PAGE 14: ...e solved (3.52, 3.53) on uniform meshes having 20, 40, and 80 elements with piecewise polynomials of uniform degrees p = 1; 2; 3; 4 and values of = 10?2, 10?6, and 10?10. Maximum errors on the (N1 =) 20-element mesh using the nite element method with the -rules and with Radau quadrature rules are presented in Table1 as functions of p, N, and . In Figure 3, we display je j1 with = 10?6 as a function of the degrees of freedom for p ranging from 1 to 4 using the -rules and Radau quadrature.... In PAGE 14: ... Finally, the nite element solution using Radau quadrature is compared with the exact solution when = 10?6, N = 20, and p = 1 to 4 in Figure 5. Finite element solutions on N1 displayed in Table1 and Figure 5 have no spurious oscillations for all cell Peclet numbers. Nodal convergence improves as p increases; however, there is an O( ) error that cannot be removed without proper resolution of the solution in the turning-point region.... ..."

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### Table 3.3. Orders of convergence with piecewise polynomials of degree k when the analytical solution u is in C([0;T]; H per(I)).

2003

Cited by 2

### TABLE 1 Errors and e ectivity indices for Example 1 using piecewise bi-p polynomial approximations.

### TABLE 10 Errors and e ectivity indices for Example 4 using piecewise bi-p polynomial approximations.

### TABLE 12 Errors and e ectivity indices for Example 5 using piecewise bi-p polynomial approximations.

### TABLE 1 Identi,cation results for the polynomial model (piecewise linear case)

### TABLE 2 Identi,cation results for the non-polynomial model (piecewise linear case)

### TABLE 5 Identi,cation results for the non-polynomial model (piecewise linear case)

### TABLE 4. Flops per grid point for truncated quadratic piecewise polynomial interpo- lation of n elds. Coord: local coordinates ^ x of departure point. Coe s: coe cients i. Derivs: derivatives. Interp: cost of interpolation. Total: total cost. Coords Coe s Derivs Interp Total

1996

"... In PAGE 43: ... of departure point. Interp: cost of interpolation. Total: total cost. TABLE4 . Flops per grid point for truncated quadratic piecewise polynomial interpo- lation of n elds.... ..."

Cited by 6