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On Finite Element Methods for Heterogeneous Elliptic Problems
Abimael F. D. Loula, Maicon R. Correa, Jo\~ao N. C. Guerreiro, Elson M. Toledo
https://arxiv.org/abs/2506.08251

On Finite Element Methods for Heterogeneous Elliptic Problems
Dealing with variational formulations of second order elliptic problems with discontinuous coefficients, we recall a single field minimization problem of an extended functional presented by Bevilacqua et al (1974), which we associate with the basic idea supporting discontinuous Galerkin finite element methods. We review residual based stabilized mixed methods applied to Darcy flow in homogeneous porous media and extend them to heterogeneous media with an interface of discontinuity. For smooth i…