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...

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell’s equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete different...

We consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, extending results previously obtained for scalar approximation. The finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element, which is then transformed to a space of vector fields on each conve...