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arXiv · 2410.15579

Intrinsic Finite Element Error Analysis on Manifolds with Regge Metrics, with Application to Calculating Connection Forms

Evan S. Gawlik·Jack McKee
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Abstract

We present some aspects of the theory of finite element exterior calculus as applied to partial differential equations on manifolds, especially manifolds endowed with an approximate metric called a Regge metric. Our treatment is intrinsic, avoiding wherever possible the use of preferred coordinates or a preferred embedding into an ambient space, which presents some challenges but also conceptual and possibly computational advantages. As an application, we analyze and implement a method for computing an approximate Levi-Civita connection form for a disc whose metric is itself approximate.

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Evan S. Gawlik, Jack McKee. 2026-06-24. Intrinsic Finite Element Error Analysis on Manifolds with Regge Metrics, with Application to Calculating Connection Forms. https://arxiv.org/abs/2410.15579

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