We present a construction of high order finite elements for H1, H(curl), H(div) (and L2) on a pyramid, which are compatible with existing tetrahedral and hexahedral high order finite elements and satisfy the commuting diagram property.

Two related approaches for solving linear systems that arise from a higher-order finite element discretization of elliptic partial differential equations are described. The first approach explores direct application of an algebraic-based multigrid method (AMG) to iteratively solve the linear systems that result from higher-order discretizations. While the choice of basis used on the discretizat...

We generalize geodesic finite elements to obtain spaces of higher approximation order. Our approach uses a Riemannian center of mass with a signed measure. We prove well-definedness of this new center of mass under suitable conditions. As a side product we can define geodesic finite elements for non-simplex reference elements such as cubes and prisms. We prove smoothness of the interpolation fu...