On 7/5/21 3:27 AM, Sylvain Mathonnière wrote:
On a side note (irrelevant now), when I was talking about orthonormal basis, I
was refering to something like \int w_i(x) w_j(x)= kronecker_{i,j}, which
should be doable and in which basis T_n^3 would look like *T_{n}^3 =
sum([T_{n}]_i^3 * w_i).*
Thank you for the clear answer, I understand my mistake now, it is much
simpler like that.
On a side note (irrelevant now), when I was talking about orthonormal
basis, I was refering to something like \int w_i(x) w_j(x)=
kronecker_{i,j}, which should be doable and in which basis T_n^3 would loo
So I applied the Crank Nicolson discretisation first before multiplying by
test functions and integrating. But then I am however confused how to handle a
term like *(T_{n}^3 * T_{n+1} , w_i)_omega*
(where *(A,B)_omega* is the usual notation for the integral over the spatial
region omega of t
I realised I made some errors in my previous post. I need an *orthonormal
*basis
of test function (not just orthogonal) to do what I claimed and even then I
have *T_{n}^3 = sum([T_{n}]_i^3 * w_i) *and then *(T_{n}^3*T_{n+1},
w_j)_omega = sum_l( T_{n+1}_l (sum_k( T_{n}_k^3 * w_k*w_l, w_j))_omeg
Thank you for your answer ! I was trying to follow the paper where they do
spatial discretisation before time discretisation, so that is why.
Why would one typically prefer to do it the other way (time discretisation
before spatial) ? I checked and it is indeed the case in the deal.II
tutorials
Sylvain,
I have not tried to follow your equations in detail, but let me point out how
this is generally done. The "right" approach is to start with the PDE, then to
use a time discretization *of the PDE* that leads to a linear occurrence of
T^{n+1} on the left hand side (possibly multiplied
