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This is a Experimental Study study.

October 16, 2025Open Access

An energy-stable parametric finite element method for the Willmore flow in three dimensions

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The new method preserves energy dissipation properties in surface evolution under the Willmore flow.
Extensive numerical experiments confirm the method's effectiveness in maintaining good mesh quality.
Insights into design and mesh quality improvement for curvature-dependent geometric flows are provided.
The first parametric finite element method for Gauss curvature flow is introduced, demonstrating significant advancements.

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This research develops an energy-stable method for Willmore and curvature-dependent flows, improving mesh quality.

Bao et al. (2025) studied this question.

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