On 4/9/19 8:51 PM, Phạm Ngọc Kiên wrote:
> I am a little bit confusing with the integral over all cell :
> *\int \varphi_i(x) *\varphi_j(x) * dx *on physical cell is approximated
> by computing *\sum { \varphi_hat_i(x_hat) *\varphi_hat_i(x_hat) *JxW(x_hat) }
> *on reference cell.
> With FEValues we get *\varphi_i(x) *, if we compute the above integral as:
> *\sum { \*varphi_i(x)* *\*varphi_j(x)* *JxW(x_hat) }*
> then the value of the integral changes because shape functions defined on
> reference cell are different from those on real cell.
>
> Is there any reason for the integral calculation*\sum { \*varphi_i(x)*
> *\*varphi_j(x)* *JxW(x_hat) }?*
I have to admit that I don't understand the question. The integral you are
computing is
\int \varphi_i(x) \varphi_j(x) dx
which is approximated using quadrature via
\sum_q \varphi_i(x_q) \varphi_j(x_q) w_q
where w_q = |det J(x_q)| \hat w_q = JxW. So this approximation happens in real
space, not on the reference cell. How the individual components are computed
(via the reference cell) is not important for the approximation.
Best
WB
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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