### Table 2: Convergence analysis for the non-smooth solution on randomly distorted meshes.

"... In PAGE 18: ...10). The numerical results shown in Table2 indicate the first-order convergence rate for concentration c. 5.... ..."

### Table 2. Non-smooth solution test problems

"... In PAGE 13: .... The test problems. We test our error estimator with the one dimensional test problems described in Tables 1 and 2. The solutions of the problems displayed in Table 1 are smooth and the ones of the problems in Table2 both have kinks at x = 1=2. Table 1.... ..."

### Table 4 Non-smooth solution: Errors and convergence rates in b.

in Mixed Finite Element Approximation of Incompressible MHD Problems Based on Weighted Regularization

### Table 3.2: Maximum non-smooth solution errors

### Table 4 Non-smooth solution: Errors and convergence rates in b.

in Mixed Finite Element Approximation of Incompressible MHD Problems Based on Weighted Regularization

2004

### Table 16. Monotone scheme on non-smooth solution test problem

### Table 3 Non-smooth solution: Errors and convergence rates in (u; p).

in Mixed Finite Element Approximation of Incompressible MHD Problems Based on Weighted Regularization

2004

"... In PAGE 30: ...1+ ( )2 H ( ). We consider the same sequence of meshes as in Section 4.1. The performance of the proposed method is shown in Table3 and Table 4; it now strongly depends on the choice of the exponent . The choice = 0 (no regularization) does not lead to convergent FEM solutions and the errors in the eld b do not decrease at all.... ..."

### Table 12. Post-processed DG method with k = 1 on non-smooth solution test problems.

### Table 17. The optimal for the monotone scheme on the non- smooth solution test problem.

"... In PAGE 24: ... Tables 16 and 17 show that the a posteriori error estimate works well in the non-smooth case. Note, in particular, in Table17 how the percentage of the grid which fails the paraboloid test is approximately halved with the grid spacing. In Figure 4.... ..."