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math.NA2025
Bounds-constrained finite element approximation of time-dependent partial differential equations
Robert C. Kirby, John D. Stephens
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-di…
math.NA2024
High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities
Robert C. Kirby, Daniel Shapero
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to…