Smoothed projections over manifolds in finite element exterior calculus
MW Licht - arXiv preprint arXiv:2310.14276, 2023 - arxiv.org
arXiv preprint arXiv:2310.14276, 2023•arxiv.org
We develop commuting finite element projections over smooth Riemannian manifolds. This
extension of finite element exterior calculus establishes the stability and convergence of
finite element methods for the Hodge-Laplace equation on manifolds. The commuting
projections use localized mollification operators, building upon a classical construction by
de Rham. These projections are uniformly bounded on Lebesgue spaces of differential
forms and map onto intrinsic finite element spaces defined with respect to an intrinsic …
extension of finite element exterior calculus establishes the stability and convergence of
finite element methods for the Hodge-Laplace equation on manifolds. The commuting
projections use localized mollification operators, building upon a classical construction by
de Rham. These projections are uniformly bounded on Lebesgue spaces of differential
forms and map onto intrinsic finite element spaces defined with respect to an intrinsic …
We develop commuting finite element projections over smooth Riemannian manifolds. This extension of finite element exterior calculus establishes the stability and convergence of finite element methods for the Hodge-Laplace equation on manifolds. The commuting projections use localized mollification operators, building upon a classical construction by de Rham. These projections are uniformly bounded on Lebesgue spaces of differential forms and map onto intrinsic finite element spaces defined with respect to an intrinsic smooth triangulation of the manifold. We analyze the Galerkin approximation error. Since practical computations use extrinsic finite element methods over approximate computational manifolds, we also analyze the geometric error incurred.
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