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The logarithmic finite element method
(International Center for Numerical Methods in Engineering (CIMNE), 2018)
The Logarithmic finite element (LogFE) method extends the Ritz-Galerkin method to approximations on a non-linear finite-dimensional manifold in the infinitedimensional solution space. Formulating the interpolant on the logarithmic space allows for a novel treatment of the rotational component of the deformation, and induces a strong coupling between rotations and translations. The Logarithmic finite element method provides a transformation of the initial configuration that is not restricted to an isoparametric formulation.
The logarithmic finite element method: Approximation on a manifold in the configuration space
(International Association for Computational IACM, 2018)