7 papers
Analysis of Bregman Proximal Point for the Obstacle Problem
Brendan Keith, Haojun Qin, Noe Reyes Rivas
We study the Bregman proximal point method for the obstacle problem, a fundamental variational inequality arising in contact mechanics, optimal design, and mathematical finance. Ea…
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…
A priori error analysis of the proximal Galerkin method
Brendan Keith, Rami Masri, Marius Zeinhofer
The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preservin…
A locally-conservative proximal Galerkin method for pointwise bound constraints
Guosheng Fu, Brendan Keith, Rami Masri
We introduce the first-order system proximal Galerkin (FOSPG) method, a locally mass-conserving, hybridizable finite element method for solving heterogeneous anisotropic diffusion…