356 IGPM356.pdf        January 2013
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