5 papers · 1 filter
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…
A Unified Framework for the Error Analysis of Physics-Informed Neural Networks
Marius Zeinhofer, Rami Masri, Kent-André Mardal
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity,…