Table 2 L 1 Errors and orders of convergence for the test case 1.

From: The piecewise parabolic method for Riemann problems in nonlinear elasticity

Scheme

N

ρ

F 11

L 1-error

L 1-order

L 1-error

L 1-order

1st order + HLL

100

2.22E-01

2.91E-02

200

1.58E-01

0.491

2.08E-02

0.489

400

1.12E-01

0.499

1.47E-02

0.497

1st order + HLLC

100

1.09E-02

5.25E-03

200

7.66E-03

0.503

3.72E-03

0.498

400

5.35E-03

0.517

2.59E-03

0.524

1st order + HLLD

100

6.97E-03

8.22E-04

200

4.89E-03

0.510

6.17E-04

0.414

400

3.01E-03

0.701

3.84E-04

0.685