finite difference method
I am implementing finite difference scheme for the simple 2D Laplace
equation. I am facing problem in imposing boundary conditions in 9-point
stencil. What boundary conditions should I give at the vertex i.e. at
the corner where two boundaries intersect.
e.g.- For square plate what should be boundary condition at four vertices?
What should be the boundary condition at vertices in Dirichlet problem?either homogeneous or non-homogeneous?
Please help in this regard.
The coupled differential equations need to solve as following:
Could you help me to discretize this systems and find the eigenvalue λ numerically using finite difference method?
Thanks in advance,
Finite Difference Method (FDM) and the related techniques such as FVM, are often found put to great use in fluid mechanics. See any simulation showing not only streamlines but also vortex shedding, turbulent mixing, etc.
Yet, when it comes to solid mechanics, Finite Element Method (FEM) is most often the method of choice. Actually, FEM is probably the *only* computational method used in solid mechanics. Most books on solid mechanics and structural analysis do not even mention FDM. A few that do, restrict FDM only to the Laplace's equation and the bi-harmonic equations--not to the general stress analysis problem in 3D.
Why is this so?