This paper develops and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity. The nonlinear equation, which was derived and analyzed by Huisken and Ilmanen in [14], represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the r...

We present a range of mesh-dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape-regular (but possibly nonquasi-uniform) meshes. These inequalities involve norms of the form �h � u� W s,p (Ω) for positive and negative s and �, where h is a function which reflects the local mesh diameter in an appropriate way. Th...

This work is concerned with the development of inverse-type inequalities for piecewise polynomial functions and, in particular, functions belonging to hp-finite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite element functions.The inequalities are explicit both in the local polynomial degree and the local mesh size.The...

This paper describes a three-dimensional parallel solution scheme for inverse dynamics of link mechanisms, which has already been proposed for the two-dimensional case and applied in several inplane motions. In this theory, the entire system is subdivided into finite elements and evaluated as a continuum. A single-link structure of a pin joint and a rigid bar is expressed using the Shifted Inte...