Changes between Version 10 and Version 11 of u/erica/norms

Timestamp:

08/22/13 16:19:37 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/norms

@@ -15 +15 @@
 == The absolute error ==
 
-If [[latex($\hat{z}$)]] is your approximate solution, and z is the exact solution, then the absolute error is just given by [[latex($E(h)=|\hat {z}-z|$)]]. This is an okay measure when z is in units scaled to a magnitude order of 1. (If not, then the error will may appear unexpectedly large or small due to scaling).
+If [[latex($\hat{z}$)]] is your approximate solution, and z is the exact solution, then the absolute error is just given by [[latex($E(h)=|\hat {z}-z|$)]]. This is an okay measure when z is in units scaled to a magnitude order of 1. (If not, then the error may appear unexpectedly large or small due to scaling).
 
 == Relative error ==
@@ -25 +25 @@
 == Note on choice ==
 
-It is often just best to scale the problem so that the measured quantities scale roughly to magnitude order of 1 (so the absolute error is a fine measure), and that the quantities are not many orders different than each other for unphysical reasons. This will help prevent bugs in numerical schemes.
+It is often just best to scale the problem so that the measured quantities scale roughly to an order of magnitude of 1 (so the absolute error is a fine measure), and that the quantities are not many orders different than each other for unphysical reasons. This will help prevent bugs in numerical schemes.
 
 = Error of vectors = 
@@ -67 +67 @@
 [[latex($e(i) = U(i) - u(x_i)$)]]
 
-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).
+However, if your numerical scheme is solving for a ''cell average'' quantity instead of just an approximation to the value of u at x_i, then obviously this error function should be adjusted. Thus, how you want to formulate e(i) depends on your scheme.
 
 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: