I have derived the weak form of the transient heat conduction equation (for FEM) and I am having trouble trying to assemble the mass matrix
This is the PDE:
[itex]
\frac{\partial U}{\partial t} = \alpha \nabla^2U
[/itex]
This is the equation for the mass matrix for an element:
[itex]
M^e = \int \Psi \Psi^T dx
[/itex]
where psi is a matrix containing the shape functions of the element.
I am quite new to FEM so I am not sure how the mass matrix is supposed to be assembled, I understand that I have to use the gauss quadrature to complete the integral but I just can't figure how the matrix containing the shape functions is assembled (i.e. I don't know what numbers go where)
Any help would be greatly appreciated.
This is the PDE:
[itex]
\frac{\partial U}{\partial t} = \alpha \nabla^2U
[/itex]
This is the equation for the mass matrix for an element:
[itex]
M^e = \int \Psi \Psi^T dx
[/itex]
where psi is a matrix containing the shape functions of the element.
I am quite new to FEM so I am not sure how the mass matrix is supposed to be assembled, I understand that I have to use the gauss quadrature to complete the integral but I just can't figure how the matrix containing the shape functions is assembled (i.e. I don't know what numbers go where)
Any help would be greatly appreciated.
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