Computation of nonclassical solutions to Hamilton-Jacobi problems

Prof. Pierre Gremaud

Department of Mathematics, North Carolina State Univesrity, Rayleigh

In this talk, we consider the construction of numerical methods for the approximation of nonclassical solutions to multidimensional Hamilton-Jacobi equations, for both scalar and vectorial problems. Recent theoretical results have yielded existence of solutions in many cases for which the usual viscosity approach was ill-suited or not applicable. The selection criterion used here is based on a viscoelasticity/capillarity approach, common in Solid Mechanics. Numerical methods adapted to this framework are built. Consistency of the model equation with the given selection criterion is essential. It is achieved through the use of high order finite difference schemes. By considering applications to potential well problems, the convergence of the methods are investigated. Joint work with Nicholas Ide.