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.

Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations / Bao, Weizhu; Garcke, Harald; Nürnberg, Robert; Zhao, Quan. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 460:(2022), pp. 11118001-11118023. [10.1016/j.jcp.2022.111180]

### Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2022
Bao, Weizhu; Garcke, Harald; Nürnberg, Robert; Zhao, Quan
Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations / Bao, Weizhu; Garcke, Harald; Nürnberg, Robert; Zhao, Quan. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 460:(2022), pp. 11118001-11118023. [10.1016/j.jcp.2022.111180]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11572/338424`