A variational treatment of the mixed boundary condition for the equilibrium diffusion equation |
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| Affiliation: | 1. CNRS and CY Cergy Paris Université, 2 rue Adolphe Chauvin, 95300 Pontoise, France;2. Department of Mathematics, New York University in Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates;3. Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan;1. Department of Mathematics, New York University Abu Dhabi, Saadiyat Island, Abu Dhabi, P.O. Box 129188, United Arab Emirates;2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA;3. Laboratoire de Mathématiques d''Orsay (UMR 8628), Université Paris-Saclay, 91405 Orsay Cedex, France;4. Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, F-31077 Toulouse, France |
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| Abstract: | We formulate the asymptotic boundary layer analysis which leads to a mixed (Robbin) boundary condition for the equilibrium diffusion equation of radiative transfer. The information required from the nonlinear boundary layer equations to obtain the boundary condition is obtained by deriving and applying an appropriate variational principle. Based upon an examination of certain limiting cases and the good accuracy previously reported in the literature for similar variational treatments, the accuracy of this variational procedure is expected to be quite good over a wide range of conditions. |
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