Hell0:

ervery one !

i want to compute the integeral of some variable over whole domain, the intergral need a high resolution gauss quadrature method, but i only have the varible value on my two dimensional grid points, the gauss quadrature need the value at the gauss quadrature points, then how should i know it.

it is a two diemsional rectangle domain. regards

maybe you should use a spectral method.

can spectral method caculate the integral

you wrote: "..I want to compute the integeral of some variable over whole domain, the intergral need a high resolution gauss quadrature method, but i only have the varible value on my two dimensional grid points, the gauss quadrature need the value at the gauss quadrature points, then how should i know it. "

I am assuming that your solution/ or your points are given in terms of a low order method, i.e. FDM or FVM. Your problem is that you want to use a high order quadrature for computing the integral (I dont know why). Of course, your quadrature point does not coincide with your FD/FV points. So, my suggestion was if you require high accuracy you should consider a high order method for example galerkin spectral method, or variations depending on your problem for computing your solution.

So, by the way why you want to use a gauss quadrature ? if you have your points uniform distributed you can use a rectangular integration rule or equilavents.

thank you very much! i am doing a Galerkin projection onto the POD eigenmode, the projection is a integral, and it is nesessary to evaluate it with a high resolution scheme! the pod eigenmode was obtained from the FVM solutions.

regards