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The finite element method is a popular method for approximating numerically on a computer the solution of partial differential equations. It is based on a variational (weak) formulation of the PDE, followed by discretization on a finite-dimensional ansatz space which reduces the problem to a sparse linear algebra one.

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Galerkin finite element method for solving third order time dependent partial differential e...

How to solve the third order time dependent partial differential equation $$u_t + 6u_x + u_xxx = 0$$ in weak form using galerkin finite element method?