Under the sole assumption of non-degeneracy of the continuous solution and the knowledge of an U-error estimate, we prove rates of convergence in measure{and in distance) for the approximate fiee boundanes, they are defined as suitable level sets, hence easy to compute The results at e apphed to the primai and mixed formulation of the obstacle problem and to singular parabohc problems {the two-...

In setting up this workshop we had to decide whether we wanted to let you become familiar with the method in a complex setting – non-linear, time-dependent calculations – or restrict ourselves to simpler problems, which allows you to get a better understanding of the method. We have chosen for the second line for several reasons: 1) The method is quite new, so it is hard to find references whic...

In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are compu...

Boundary integral equations are a classical tool for the analysis of boundary value problems for partial differential equations. The term “ boundary element method” (BEM) denotes any method for the approximate numerical solution of these boundary integral equations. The approximate solution of the boundary value problem obtained by BEM has the distinguishing feature that it is an exact solution...

Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general settings, the advantageous features of Rayleigh–Ritz methods such as the avoidance of discrete compatibility conditions and the production of symmetric and positive definite discrete systems. The methods are...

Stability parameters for stabilized methods in uids are suggested. The computation of the largest eigenvalue of a generalized eigenvalue problem replaces controversial de nitions of element diameters and inverse estimate constants, used heretofore to compute these stability parameters. The design is employed in the advective-di usive model, incompressible Navier-Stokes equations and the Stokes ...