Free boundaries and finite elements in one dimension

Free Boundaries and Finite Elements in One Dimension

Two problems in control theory, one with state constraints and the other with control constraints, have been approximated by the finite element method. This discretization has been applied to both the primal and the dual formulation, in order to make a number of observations and comparisons: 1. The rate of convergence as the grid interval h is decreased, for polynomial elements of different deg...

Covering dimension and finite-to-one maps

To Ken Kunen on the occasion of his retirement from teaching MSC: primary 54F45 secondary 54C10, 54G05

On Completely Free Elements in Finite Fields

Simulations of transport in one dimension

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Structure of One-phase Free Boundaries in the Plane

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Hauswirth, Hélein and Pacard, whose free boundary has the shape of a double hairp...