When Bingham meets Bratu: mathematical and computational investigations

نویسندگان

چکیده

In this article, we discuss the numerical solution of Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with total variation integral and an exponential nonlinearity. Using fact that one can view as possible Lagrange multiplier constrained minimization from Calculus Variations, associate BBG initial value (dynamical flow), well suited to time-discretization by operator-splitting. Various mathematical results are proved, including convergence finite element approximation problem. The operator-splitting/finite methodology discussed in article is robust easy implement. We validate implementation first solving classical Bratu-Gelfand obtaining reporting consistent those found literature. then explore full capability viscoplastic for several values plasticity yield. conclude exhibiting discussing bifurcation diagrams corresponding these same yield, examining some finer details solver discovered during course our investigation.

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ژورنال

عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations

سال: 2021

ISSN: ['1262-3377', '1292-8119']

DOI: https://doi.org/10.1051/cocv/2021020