Numerical experiments with FEMLAB® to support mathematical research

Nedanstående innehåll är skapat av Mimers Brunns besökare. Kommentera arbete

Using the finite element software FEMLAB® solutions are computed to Dirichlet problems for the Infinity-Laplace equation ?8(u) = u2xuxx + 2uxuyuxy + u2yuyy = 0. For numerical reasons ?q(u) = div (|?u|q?u) = 0, which (formally) approaches as ?8(u) = 0 as q ? 8, is used in computation. A parametric nonlinear solver is used, which employs a variant of the damped Newton-Gauss method. The analysis of the experiments is done using the known theory of solutions to Dirichlet problems for ?8(u) = 0, which includes AMLEs (Absolutely Minimizing Lipschitz Extensions), sets of uniqueness, critical segments and lines of singularity. From the experiments one main conjecture is formulated: For Dirichlet problems, which have a non-constant boundary function, it is possible to predict the structure of the lines of singula...