I am interested to study crack propagation in a hyperelastic material in a variational setting. The crack surface exhibits a jump discontinuity. The function space for displacement field should consist of discontinuous functions.
The discontinuous galerkin finite element (DGFEM) approximation space consist of piecewise discontinuous functions which seems to a valid choice to solve crack problem. However, the required degree of freedom is extremely large for a high resolution discretization.
The recently proposed, enriched galerkin finite element method (EGFEM) enriched the continuous galerkin approximation space with a piecewise constant function. This allows discontinuities along the element face. For example, a one dimensional function $f(x)$ can be approximated in a unit interval as,
$ f(x) = f_1 \phi_1(x) + f_2 \phi_2(x) + f_3$
where $\phi_1(x)$ and $\phi_2(x)$ are basis functions. EGFEM seems to be a better choice to solve crack problem as required degree of freedom is quite less than for DGFEM.
EGFEM does introduce the discontinuity along the edges/faces, but in the deformed configuration the disjoint edges/faces would always be parallel. This is one of the limitation of EGFEM.
Before going to implement these methods, I would like to understand advantage and disadvantage of DGFEM and EGFEM approach to solve the hyperelastic energy minimization problem.
What all points I should consider to evaluate these methods ?