Title: Weak Solution of PDE
1Weak 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)
2Sergey Lvovich Sobolev (1908-1989) ,
Soviet-Russian a founder of the approach
generalized derivatives and generalized solution
3Sobolev Space
4Generalized solution of the steady state
boundary problem second order PDE
5Implementation 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
6Generalized solution of the time dependent
Initial Boundary Problem (IBP) for second order
diffusive equation
7Implementation 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