Proximal Galerkin method exactly enforces the isometry constraint for nonlinear plates at mesh cell barycenters without preprocessing, yielding asymptotically mesh-independent convergence.
arXiv preprint arXiv:2507.13516 (2025)
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A new family of proximal DG methods for variational inequalities is proposed, with the hybrid high-order variant achieving the first higher-order convergence for proximal Galerkin methods.
The proximal Galerkin method reformulates phase-field fracture constraints into saddle-point problems to enforce physical bounds and irreversibility for static and dynamic cases.
A structure-preserving LDG discretization with backward Euler for conformational conversion systems that enforces positivity, proves entropy stability and convergence, and yields existence of global weak solutions.
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Proximal Galerkin for the isometry constraint
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