Finite Element for PDE having both spatial and temporal Derivatives

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Can anyone guide or suggest any examples for implementing the finite element method to 1D PDEs that have both temporal and spatial partial derivatives? Im having trouble understanding the FEM so a simple example that shows how to make a state space matrix from the FEM discretization would be helpful.

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Am not sure what you are asking, but any textbook covering finite element method am sure you will find an example implementing the finite element method. You might google search finite element method for the heat equation as it has both spatial derivate and temporal derivative.