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.
Petryk, A quasi-extremal energy principle for non-potential problems in rate-independent plasticity, Journal of the Mechanics and Physics of Solids 136 (2020) 103691
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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.