{"title":"Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.</jats:p>"}],"issue":"1","intvolume":"       151","date_updated":"2024-04-03T09:19:34Z","volume":151,"department":[{"_id":"841"}],"publication_status":"published","date_created":"2023-07-10T11:43:44Z","doi":"10.1007/s00211-022-01280-5","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"first_name":"Cedric Aaron","full_name":"Beschle, Cedric Aaron","last_name":"Beschle"},{"orcid":"0000-0001-9872-3474","id":"100441","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs"}],"publication":"Numerische Mathematik","page":"1-48","language":[{"iso":"eng"}],"citation":{"chicago":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i> 151, no. 1 (2022): 1–48. <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">https://doi.org/10.1007/s00211-022-01280-5</a>.","mla":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i>, vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>.","apa":"Beschle, C. A., &#38; Kovács, B. (2022). Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>, <i>151</i>(1), 1–48. <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">https://doi.org/10.1007/s00211-022-01280-5</a>","short":"C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.","ieee":"C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces,” <i>Numerische Mathematik</i>, vol. 151, no. 1, pp. 1–48, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>.","bibtex":"@article{Beschle_Kovács_2022, title={Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48} }","ama":"Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>. 2022;151(1):1-48. doi:<a href=\"https://doi.org/10.1007/s00211-022-01280-5\">10.1007/s00211-022-01280-5</a>"},"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"publisher":"Springer Science and Business Media LLC","status":"public","_id":"45958","user_id":"100441","year":"2022"}