Generalized Park-Sheen Finite Elements for Adaptivity

Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection-diffusion

A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.

On Hanging Node Constraints for Nonconforming Finite Elements using the Douglas-Santos-Sheen-Ye Element as an Example

On adaptively refined quadrilateral or hexahedral meshes, one usually employs constraints on degrees of freedom to deal with hanging nodes. How these constraints are constructed is relatively straightforward for conforming finite element methods: The constraints are used to ensure that the discrete solution space remains a subspace of the continuous space. On the other hand, for nonconforming m...

Alfred Sheen

Quadratic serendipity finite elements on polygons using generalized barycentric coordinates

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence....

Hybrid Stochastic Finite Elements and Generalized Monte Carlo Simulation