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Weak Solution of PDE

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... Derivatives. This definition is well posed in a sense, that if function has a classical ... Generalized derivative exist and almost every where equal ... – PowerPoint PPT presentation

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Title: Weak Solution of PDE


1
Weak Solution of PDE
Generalized Derivatives
This definition is well posed in a sense, that if
function has a classical derivative then
Generalized derivative exist and almost every
where equal generalized equation ( Home Work,
prove this result)
2
Sergey Lvovich Sobolev (1908-1989) ,
Soviet-Russian a founder of the approach
generalized derivatives and generalized solution
3
Sobolev Space
4
Generalized solution of the steady state
boundary problem second order PDE
5
Implementation on FEMLAB a week formulation for
Elliptic PDE
Always be careful in choosing sign in weak
formulation check with respect to situation when
you have an analytical solution
6
Generalized solution of the time dependent
Initial Boundary Problem (IBP) for second order
diffusive equation
7
Implementation on FEMLAB a week formulation for
Parabolic PDE
Always be careful in choosing sign in weak
formulation check with respect to situation when
you have an analytical solution
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