{"product_id":"9783658525453","title":"Discretely Divergence-Free Q2-P1 Finite Elements for Incompressible Flow Problems A Geometric Multigrid Approach for Solving the Three-Dimensional Navier-Stokes Equations","description":"\u003ch1\u003eDiscretely Divergence-Free Q2-P1 Finite Elements for Incompressible Flow Problems\u003c\/h1\u003e\u003ch2\u003eA Geometric Multigrid Approach for Solving the Three-Dimensional Navier-Stokes Equations\u003c\/h2\u003e\u003ch3\u003eChristoph Lohmann\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Differential Equations \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cp\u003eDiscretely divergence-free finite elements are characterized by vector-valued shape functions that satisfy the discrete incompressibility condition in an a priori manner. When applied to the incompressible Navier-Stokes equations, this approach yields a problem defined solely for the velocity field, thereby avoiding the typical saddle-point structure of mixed formulations. Consequently, iterative solvers do not require adaptation to a zero block and highly efficient solution strategies become available.\u003cbr\u003eIn this book, Christoph Lohmann exploits this concept to develop a geometric multigrid solver for three-dimensional flow problems. The proposed method achieves a mesh-independent convergence behavior under standard assumptions, while its performance is validated in several linear and nonlinear test cases. Numerical examples demonstrate the necessity of using so called `global' finite element functions to accurately predict the flow behavior through geometries with multiple connected branches. These functions can be implicitly incorporated into the proposed multigrid framework using suitable filtering techniques.\u003c\/p\u003e\u003c\/div\u003e\u003cdiv\u003e\u003cp\u003eChristoph Lohmann is a postdoctoral researcher in the Department of Mathematics at TU Dortmund University. His research interests include finite element methods satisfying discrete maximum principles, parallel-in-time methods, and efficient solvers for incompressible flow problems.\u003c\/p\u003e\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e09 August 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Fachmedien Wiesbaden\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer Spektrum\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783658525453\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e127\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Fachmedien Wiesbaden","offers":[{"title":"Default Title","offer_id":51043024371852,"sku":"9783658525453","price":76.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783658525453.jpg?v=1782525381","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783658525453","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}