A Parametric Finite Element Approach for an Anisotropic Multi-Phase Mullins-Sekerka Problem with Kinetic Undercooling

Mathematics > Numerical Analysis [Submitted on 20 Feb 2026 (v1), last revised 18 Jun 2026 (this version, v2)] Title:A Parametric Finite Element Approach for an Anisotropic Multi-Phase Mullins-Sekerka Problem with Kinetic Undercooling View PDF HTML (experimental)Abstract:We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum of the volumes of the enclosed phases decreases in time. Upon deriving a suitable variational formulation, we introduce a fully discrete unfitted finite element method. In this approach, the approximations of the moving interfaces are independent of the triangulations used for the equations in the bulk. Our method can be shown to be unconditionally stable. Several numerical examples demonstrate the capabilities of the introduced method. In particular, it is demonstrated that the evolution of multiple ice crystals with junctions can be modeled using the proposed approach. Submission history From: Tokuhiro Eto [view email][v1] Fri, 20 Feb 2026 14:06:57 UTC (1,306 KB) [v2] Thu, 18 Jun 2026 13:53:05 UTC (1,313 KB) Current browse context: math.NA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.