356	RWTH Publication No: 230325        2013        IGPM356.pdf
TITLE	Geodesic Finite Elements of Higher Order
AUTHORS	Oliver Sander
ABSTRACT	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 functions, and various invariance properties. Numerical tests show that the optimal convergence orders of the discretization error known from the linear theory are obtained also in the nonlinear setting.
KEYWORDS	Geodesic finite elements, higher order, manifold, Riemannian center of mass, signed measure, liquid crystals, unit sphere
DOI	10.1093/imanum/drv016
PUBLICATION	IMA Journal Numerical Analysis 2016, 36, 1, pp 238-266