Gockenbach has some good PDE books that include FEM treatments that are at a comparable math level. One on PDE with some basic theory, analytic methods & FEM, and one dedicated to FEM. Both are on SIAM press.
________________________________________ From: [email protected] [[email protected]] on behalf of Nikolaus Rath [[email protected]] Sent: Thursday, January 09, 2014 5:37 PM To: Anders Logg Cc: Jan Blechta; [email protected] Subject: Re: [FEniCS] Solving equation without Boundary Conditions? On 01/09/2014 03:00 PM, Anders Logg wrote: > On Thu, Jan 09, 2014 at 09:00:38PM +0100, Jan Blechta wrote: >> On Thu, 9 Jan 2014 11:26:09 -0800 >> Nikolaus Rath <[email protected]> wrote: >> >>> On 01/09/2014 11:19 AM, Jan Blechta wrote: >>>>> So if I understand correctly, I don't need to do anything special >>>>> for >>>>>> the boundary conditions because Dolfin assumes Neumann by >>>>>> default, and Neumann conditions are only reflected in L. >>>> This is not true - DOLFIN does not assume. It is a property of this >>>> variational problem. >>> Huh? Maybe we misunderstood each other, but >>> http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/neumann-poisson/python/documentation.html >>> says: >>> >>> "Since we have natural (Neumann) boundary conditions in this problem, >>> we don´t have to implement boundary conditions. This is because >>> Neumann boundary conditions are default in DOLFIN." >> So this is basically wrong (probably written by some graduate >> student). > This sentence was indeed written by a student but I would not say that > it is wrong. This problem does use natural boundary conditions which > in this case are of Neumann type and for that reason, one does not > need to impose boundary conditions explicitly. > > But I agree that if one just reads that single sentence it is somewhat > misleading. It does not mean one does not need to think about the > boundary conditions or take special measures to implement them > correctly. If one reads the rest of the page, there is a long > discussion on exactly this issue: which measures have to be taken to > solve the pure Neumann problem. Alright, reading these messages it seems my understanding of PDE theory is a bit rusty. Could someone give me a literature recommendation that will help me understand this discussion? My current understanding is on the level of "Mathematical Methods for Physicists" from Arfken & Weber, "Applied PDEs" from Habermann or "Classical Electrodynamics" from Jackson (they all elaborate on Dirichlet vs Neumann conditions, but none of them seem to say anything about essential vs natural). Best, Nikolaus -- Nikolaus Rath, Ph.D. Senior Scientist Tri Alpha Energy, Inc. +1 949 830 2117 ext 211 _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
