Proximal Galerkin method exactly enforces the isometry constraint for nonlinear plates at mesh cell barycenters without preprocessing, yielding asymptotically mesh-independent convergence.
Proximal Discontinuous Galerkin Methods for Variational Inequalities
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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 born from applying a different well-known nonconforming finite element discretization to the Bregman proximal point method. We explicitly treat four examples: the symmetric interior penalty discontinuous Galerkin, the enriched Galerkin, the hybridizable interior penalty and the hybrid high-order methods. We formulate a unified analysis framework for this family of methods and prove the existence and uniqueness of solutions, energy dissipation, and error estimates for both the primal and dual variables. Remarkably, the proximal hybrid high-order method with piecewise constant cell unknowns and piecewise affine facet unknowns leads to the first higher-order convergence result for any proximal Galerkin method.
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math.NA 2years
2026 2representative citing papers
The proximal Galerkin method reformulates phase-field fracture constraints into saddle-point problems to enforce physical bounds and irreversibility for static and dynamic cases.
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Proximal Galerkin for the isometry constraint
Proximal Galerkin method exactly enforces the isometry constraint for nonlinear plates at mesh cell barycenters without preprocessing, yielding asymptotically mesh-independent convergence.
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Proximal Galerkin for Phase Field Fracture
The proximal Galerkin method reformulates phase-field fracture constraints into saddle-point problems to enforce physical bounds and irreversibility for static and dynamic cases.