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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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Boundary integration of weak form in FEM using DG elements

If we use CG elements (continuous Galerkin), the boundary integration in FEM can be easily converted to sum over quadrature points using node basis functions of the edges. However, in DG elements (dis …