Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce and analyze several new finite element schemes for fourth order geometric evolution equations in an axisymmetric setting, and for selected schemes we will show existence, uniqueness and stability results. The presented schemes have very good mesh and stability properties, as will be demonstrated by several numerical examples.

Finite element methods for fourth order axisymmetric geometric evolution equations / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 376:(2019), pp. 733-766. [10.1016/j.jcp.2018.10.006]

Finite element methods for fourth order axisymmetric geometric evolution equations

Nürnberg R.
2019-01-01

Abstract

Fourth order curvature driven interface evolution equations frequently appear in the natural sciences. Often axisymmetric geometries are of interest, and in this situation numerical computations are much more efficient. We will introduce and analyze several new finite element schemes for fourth order geometric evolution equations in an axisymmetric setting, and for selected schemes we will show existence, uniqueness and stability results. The presented schemes have very good mesh and stability properties, as will be demonstrated by several numerical examples.
2019
Barrett, J. W.; Garcke, H.; Nürnberg, R.
Finite element methods for fourth order axisymmetric geometric evolution equations / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 376:(2019), pp. 733-766. [10.1016/j.jcp.2018.10.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/283437
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