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To obtain a numerical method to compute a solution approximation we
start by deriving a variational statement of our problem at
hand.
Multiply (1) by a test function
and integrate i.e.
|
(4) |
As usual we assume to be smooth enough to allow us to integrate by
parts. We get
|
(5) |
Since and we thus obtain
|
(6) |
Hence, the variational formulation of (1) reads: Find
such that for every fixed time
for all and .
Mohammad Asadzadeh
2004-08-27