{"title":"Compatible Finite Elements for Glacier Modeling","authors":"D. Brinkerhoff","doi":"10.1109/MCSE.2023.3305864","DOIUrl":null,"url":null,"abstract":"Described in this article is the first application of two mixed finite-element methods to the equations of glacier evolution under different simplifying assumptions, along with a framework for the implicit solution of the coupled velocity-thickness equations. The first method uses Raviart–Thomas elements for velocity and piecewise constants for thickness and is a reframing of a classic staggered-grid finite-difference method to the case of unstructured triangular meshes. The second method uses Mardal–Tai–Winther elements for velocity and exhibits several desirable properties: second-order convergence of velocity and near-exact mass conservation while resolving both membrane and shear stresses in steep topography with thin ice.","PeriodicalId":10553,"journal":{"name":"Computing in Science & Engineering","volume":"25 1","pages":"18-28"},"PeriodicalIF":1.8000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computing in Science & Engineering","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1109/MCSE.2023.3305864","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
Described in this article is the first application of two mixed finite-element methods to the equations of glacier evolution under different simplifying assumptions, along with a framework for the implicit solution of the coupled velocity-thickness equations. The first method uses Raviart–Thomas elements for velocity and piecewise constants for thickness and is a reframing of a classic staggered-grid finite-difference method to the case of unstructured triangular meshes. The second method uses Mardal–Tai–Winther elements for velocity and exhibits several desirable properties: second-order convergence of velocity and near-exact mass conservation while resolving both membrane and shear stresses in steep topography with thin ice.
期刊介绍：
Physics, medicine, astronomy -- these and other hard sciences share a common need for efficient algorithms, system software, and computer architecture to address large computational problems. And yet, useful advances in computational techniques that could benefit many researchers are rarely shared. To meet that need, Computing in Science & Engineering presents scientific and computational contributions in a clear and accessible format.
The computational and data-centric problems faced by scientists and engineers transcend disciplines. There is a need to share knowledge of algorithms, software, and architectures, and to transmit lessons-learned to a broad scientific audience. CiSE is a cross-disciplinary, international publication that meets this need by presenting contributions of high interest and educational value from a variety of fields, including—but not limited to—physics, biology, chemistry, and astronomy. CiSE emphasizes innovative applications in advanced computing, simulation, and analytics, among other cutting-edge techniques. CiSE publishes peer-reviewed research articles, and also runs departments spanning news and analyses, topical reviews, tutorials, case studies, and more.
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