4 papers · 2 filters
Proximal Galerkin for the isometry constraint
Brendan Keith, Frédéric Marazzato
We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, th…
Proximal Galerkin for Phase Field Fracture
Miguel Castillón, Biswajit Khara, Jørgen S. Dokken +3
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of…
Proximal Discontinuous Galerkin Methods for Variational Inequalities
Alexandre Ern, Brendan Keith, Dohyun Kim +2
We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is…
The proximal Galerkin method for non-symmetric variational inequalities
Guosheng Fu, Brendan Keith, Dohyun Kim +2
We introduce the proximal Galerkin (PG) method for non-symmetric variational inequalities. The proposed approach is asymptotically mesh-independent and yields constraint-preserving…