{"date_updated":"2024-04-03T09:15:44Z","status":"public","date_created":"2023-07-10T11:47:11Z","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.</jats:p>","lang":"eng"}],"intvolume":"       151","_id":"45969","page":"873-925","publication_status":"published","keyword":["Applied Mathematics","Computational Mathematics"],"type":"journal_article","language":[{"iso":"eng"}],"user_id":"100441","title":"Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces","year":"2022","doi":"10.1007/s00211-022-01301-3","citation":{"short":"C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.","ama":"Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>. 2022;151(4):873-925. doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>","apa":"Elliott, C. M., Garcke, H., &#38; Kovács, B. (2022). Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>, <i>151</i>(4), 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>","ieee":"C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces,” <i>Numerische Mathematik</i>, vol. 151, no. 4, pp. 873–925, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","chicago":"Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i> 151, no. 4 (2022): 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>.","mla":"Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","bibtex":"@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces}, volume={151}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs}, year={2022}, pages={873–925} }"},"publication":"Numerische Mathematik","author":[{"full_name":"Elliott, Charles M.","last_name":"Elliott","first_name":"Charles M."},{"last_name":"Garcke","full_name":"Garcke, Harald","first_name":"Harald"},{"full_name":"Kovács, Balázs","last_name":"Kovács","id":"100441","orcid":"0000-0001-9872-3474","first_name":"Balázs"}],"department":[{"_id":"841"}],"publisher":"Springer Science and Business Media LLC","publication_identifier":{"issn":["0029-599X","0945-3245"]},"issue":"4","volume":151}