Finite elements on the sphere

On the Displacement-Stress Continuous Finite Elements

For the analysis of composite media, three different compatible and mixed finite element formulations are presented which apriori enforce the continuity of stresses as well as displacements at the element interfaces. The formulations are applied for the analysis of hi-material interfaces in two problems often encountered in the field of orthopaedic biomechanics, that is the fixation analysis in...

Finite Differencing on the Sphere

We describe a finite difference version of the eth formalism, which allows use of spherical coordinates in 3-dimensional systems with global second order accuracy. We briefly present the application of the formalism to the evolution of linear scalar waves and to the calculation of the curvature scalar of a curved geometry on a topologically spherical manifold.

Finite Sphere Packings and Sphere Coverings

Finite Differences on t he Sphere

Even before any numerical considerations are confronted, we run into difficulties simply in specifying a coordinate system. It is important to distinguish between true scalarvalued and vector-valued functions. The value of a scalar function, say temperature, is independent of coordinate system. That is, the temperature at some point in space is the same regardless of how we define the position ...

Finite elements on evolving surfaces

In this article, we define a new evolving surface finite-element method for numerically approximating partial differential equations on hypersurfaces Γ (t) in Rn+1 which evolve with time. The key idea is based on approximating Γ (t) by an evolving interpolated polyhedral (polygonal if n = 1) surface Γh(t) consisting of a union of simplices (triangles for n = 2) whose vertices lie on Γ (t). A fi...