Bao, Weizhu and Garcke, Harald and Nurnberg, Robert and Zhao, Quan (2022) Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations. JOURNAL OF COMPUTATIONAL PHYSICS, 460: 111180. ISSN 0021-9991, 1090-2716
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We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of the generating curves of the axisymmetric surfaces. The proposed numerical methods are based on piecewise linear parametric finite elements. The constructed fully practical schemes satisfy the conservation of the enclosed volume. In addition, we prove the unconditional stability and consider the distribution of vertices for the discretized schemes. The introduced methods are implicit and the resulting nonlinear systems of equations can be solved very efficiently and accurately via the Newton's iterative method. Numerical results are presented to show the accuracy and efficiency of the introduced schemes for computing the considered axisymmetric geometric flows.(c) 2022 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | STATE DEWETTING PROBLEMS; SHARP-INTERFACE MODEL; SURFACE-DIFFUSION; WILLMORE FLOW; APPROXIMATION; MOTION; STABILITY; DYNAMICS; Surface diffusion flow; Conserved mean curvature flow; Parametric finite element method; Axisymmetry; Volume conservation; Unconditional stability |
| Subjects: | 500 Science > 500 Natural sciences & mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Jan 2024 13:45 |
| Last Modified: | 30 Jan 2024 13:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57679 |
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