The authors extend their prior dual (Lagrange multiplier) variational framework to steady and transient convection-diffusion and heat equations, discretizing with B-splines or RePU networks, and report numerical accuracy with observed convergence rates.
Gurtin, Variational principles for linear initial-value problems, Quarterly of Applied Mathematics 22 (3) (1964) 252–256
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Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants
The authors extend their prior dual (Lagrange multiplier) variational framework to steady and transient convection-diffusion and heat equations, discretizing with B-splines or RePU networks, and report numerical accuracy with observed convergence rates.