| | 62 | |
| | 63 | = Error of GRID functions = |
| | 64 | |
| | 65 | Grid functions are the result of solving a discretized finite difference scheme or the like. They are given by a dicretized function, U(i). To compute the error norm of a grid function, we must first define an appropriate discretized error function, e(i). One choice could be, |
| | 66 | |
| | 67 | [[latex($e(i) = U(i) - u(x_i)$)]] |
| | 68 | |
| | 69 | However, if your numerical scheme is solving for a ''cell average'' quantity instead of just an approximation to the value of u at xi, then obviously this error function should be adjusted. Thus, it depends on your scheme how you want to formulate e(i). |
| | 70 | |
| | 71 | Once e(i) is formulated, the norms are now discretized versions of the integral formulas of the previous section. Taking a discretized sum now, and substituting dx=h=L/mx+1, where L is the domain length and mx is the number of computing cells, we have: |
| | 72 | |
| | 73 | |
