%0 Book %1 dipietro2012mathematical %A Di Pietro, Daniele A. %A Ern, Alexandre %B Mathématiques et Applications %C Berlin %D 2012 %I Springer %K 35q30-navier-stokes-equations 65-02-numerical-analysis-research-exposition 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m50-pdes-ibvps-mesh-generation-and-refinement 65m60-pdes-ibvps-finite-elements 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n30-pdes-bvps-finite-elements 65n50-pdes-bvps-mesh-generation-and-refinement 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 76m12-finite-volume-methods-in-fluid-mechanics 76r50-diffusion 80m25-heat-transfer-other-numerical-methods discontinuous-galerkin %R 10.1007/978-3-642-22980-0 %T Mathematical Aspects of Discontinuous Galerkin Methods %U https://link.springer.com/book/10.1007%2F978-3-642-22980-0 %V 69 %X This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite-element and finite-volume viewpoints are utilized to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed. %@ 9783642229794

@book{dipietro2012mathematical, abstract = {This book introduces the basic ideas for building discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. It is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite-element and finite-volume viewpoints are utilized to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Berlin}, author = {Di Pietro, Daniele A. and Ern, Alexandre}, biburl = {https://www.bibsonomy.org/bibtex/28bbe1f4714f8551f31a36532f4464eb1/gdmcbain}, citeulike-article-id = {11655915}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-642-22980-0}, citeulike-linkout-1 = {http://www.worldcat.org/isbn/9783642229794}, citeulike-linkout-2 = {http://books.google.com/books?vid=ISBN9783642229794}, citeulike-linkout-3 = {http://www.amazon.com/gp/search?keywords=9783642229794\&index=books\&linkCode=qs}, citeulike-linkout-4 = {http://www.librarything.com/isbn/9783642229794}, citeulike-linkout-5 = {http://www.worldcat.org/oclc/761012811}, comment = {(private-note)BUMPC MIR: 79 DIP 12}, doi = {10.1007/978-3-642-22980-0}, interhash = {4785629f61b9130b411054a6024aa3e6}, intrahash = {8bbe1f4714f8551f31a36532f4464eb1}, isbn = {9783642229794}, issn = {1154-483X}, keywords = {35q30-navier-stokes-equations 65-02-numerical-analysis-research-exposition 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m50-pdes-ibvps-mesh-generation-and-refinement 65m60-pdes-ibvps-finite-elements 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods 65n30-pdes-bvps-finite-elements 65n50-pdes-bvps-mesh-generation-and-refinement 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics 76m12-finite-volume-methods-in-fluid-mechanics 76r50-diffusion 80m25-heat-transfer-other-numerical-methods discontinuous-galerkin}, posted-at = {2012-11-09 14:29:42}, priority = {2}, publisher = {Springer}, series = {Mathématiques et Applications}, timestamp = {2021-06-07T03:13:51.000+0200}, title = {Mathematical Aspects of Discontinuous {G}alerkin Methods}, url = {https://link.springer.com/book/10.1007%2F978-3-642-22980-0}, volume = 69, year = 2012 }