Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 389, Issue -, Pages 48-61Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.03.006
Keywords
Tensor fields; Surface PDEs; Finite element method; Liquid crystals
Funding
- German Research Foundation (DFG) [Vo899-19]
- Julich Supercomputing Centre [HDR06]
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We derive a Cartesian componentwise description of the covariant derivative of tangential tensor fields of any degree on Riemannian manifolds. This allows to reformulate any vector-and tensor-valued surface PDE in a form suitable to be solved by established tools for scalar-valued surface PDEs. We consider piecewise linear Lagrange surface finite elements on triangulated surfaces and validate the approach by a vector- and a tensor-valued surface Helmholtz problem on an ellipsoid. We experimentally show optimal (linear) order of convergence for these problems. The full functionality is demonstrated by solving a surface Landau-de Gennes problem on the Stanford bunny. All tools required to apply this approach to other vector- and tensor-valued surface PDEs are provided. (C) 2019 Elsevier Inc. All rights reserved.
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