Hi,
In FEM, I imposed the Dirichlet as essential and Neumann as natural boundary conditions for the heat equation with some specific values. My question is : Once the solution is obtained for the temperature distribution, how to know whether the boundary condition is satisfied or not? As far as Dirichlet boundary condition is concerned, it satisfies exactly with respect to the domain since it is explicitly applied and in the solution, the values are same. What about Neumann Boundary condition?
Very detailed explanations have been given in the answers to the related question:
https://www.researchgate.net/post/What_is_the_difference_between_essential_boundary_conditions_and_natural_boundary_conditions
In a nutshell, I think finite elements are not guaranteed to satisfy Neumann boundary conditions exactly in the general case. The boundary conditions will be recovered exactly if the assumed solution space (as defined by the shape functions) contains the exact solution (see e.g. 'patch test').
By the way, even Dirichlet b.c. are interpolated by the shape functions along the boundary and are only imposed exactly at the nodes. Hence, strictly speaking, whether or not they are satisfied exactly also depends on whether they can be represented by the shape functions (which is usually the case).
Dear Sunag Rattehalli Amaranath
Read the following book may be help you
"Nonlinear Finite Element Analysis of Solids and Structures" for René De Borst
@Amaranath
Simple way is to plot the solution. Then you will know your requirement.
B.Rath
Mr. Rath has the simplest and practical solution as I have done with MATLAB and/or Algor.
@Joseph
Thank you for accepting my simple approach.
I feel you have done some work in numerical analysis. Do you time to help me in writting Zeta function ?
Prof B.Rath
True you can just plot your solution, and see the values of derivatives, etc, there. Mr. Rath's approach is practical.
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