Krishna, Have a look at step-7 for Neumann boundary conditions, step-15 for nonlinear problems and step-26 for time-dependent problems to get started. Let us know if you have more specific questions.
Best, Daniel Am Do., 12. März 2020 um 17:38 Uhr schrieb Krishnakumar Gopalakrishnan < [email protected]>: > I need to solve the following non-linear diffusion equation on a unit 1D > domain: > > du/dt = \nabla \dot ( D(u) \grad u) > > subject to Neumann bcs at both ends. D(u)*grad(u) = f(t) at x=0, and > D(u)*grad(u) = 0 at x=1, with a constant initial condition u(x,0) = u0 > > The difficulty with this problem is two fold > > - The diffusion coefficient D is a function of the field variable u, > - Diffusion coefficient D(u) varies by 4 orders of magnitute between > 10^-12 and 10^-16 > > Being 1D, the problem size is very small and I am thnking of just using > direct solvers. However, I don't quite know how to start approaching this > problem and how to begin the coding this in deal.ii. > > I'd appreciate any thoughts/help/suggestions/guidance from the deal.II > community. > > Regards, > Krishna > > > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/3c0a13b9-1d59-443d-97bf-5a95440281d3%40googlegroups.com > <https://groups.google.com/d/msgid/dealii/3c0a13b9-1d59-443d-97bf-5a95440281d3%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CAOYDWbK8fuCwiTQPjKO%2BaNhtLeAvCtXonskzS5%2BBha8CEkjw3w%40mail.gmail.com.
