L1,L2, .. L_infinity Errors ??

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 November 12, 2010, 06:44 L1,L2, .. L_infinity Errors ?? #1 New Member   Elmiloud Chaabelasri Join Date: Oct 2010 Posts: 27 Rep Power: 8 Hello, Can you tell me how can calculate the L1,L2 .. Errors, I used a Roe solver with triangular mesh. Thanks in advance.

 November 12, 2010, 13:25 #2 New Member   Join Date: May 2009 Posts: 28 Rep Power: 9 You have to (numerically) integrate over all elements in the mesh and sum up the computed contributions from each element, e.g. $\sum_T \int_T (u-u_h)^2 dx$ for the L^2 error. What you do on each element of the mesh is iterating over integration points. At each integration point you have to evaluate shape functions, compute u_h using the coefficients from your solution vector, evaluate (u-u_h)^2, add this to err with the proper weight and integration element and so on and so forth... This is standard and should be described in all books used for teaching. Some pseudocode Code: errl2 = 0; for T in mesh for q in quad(T) eval(phi, q); // shape functions u_h=dot_product(phi, coeff(T)); x = T.local_to_global(q.position); eval(u, x); errl2loc = u-u_h; errl2 = errl2 + (errl2loc^2)*q.weight*T.det; end end

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