Compatible Spatial Discretizations / SpringerLink (Online service) ; Douglas N. Arnold ; Pavel B. Bochev ; Richard B. Lehoucq ; Roy A. Nicolaides ; Shashkov, Mikhail (2006)  

Público ISBD Título : Compatible Spatial Discretizations Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Douglas N. Arnold ; Pavel B. Bochev ; Richard B. Lehoucq ; Roy A. Nicolaides ; Shashkov, Mikhail Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: The IMA Volumes in Mathematics and its Applications, ISSN 0940-6573 num. 142 Número de páginas: XIV, 247 p Il.: online resource ISBN/ISSN/DL: 978-0-387-38034-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Partial  differential  equations  Applied  mathematics  Engineering  Numerical  analysis  Applications  of  Differential  Equations  Analysis Clasificación: 51 Matemáticas Resumen: The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/ Nota de contenido: Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions -- Differential Complexes and Stability of Finite Element Methods I. The de Rham Complex -- Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex -- On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems -- Principles of Mimetic Discretizations of Differential Operators -- Compatible Discretizations for Eigenvalue Problems -- Conjugated Bubnov-Galerkin Infinite Element for Maxwell Equations -- Covolume Discretization of Differential Forms -- Mimetic Reconstruction of Vectors -- A Cell-Centered Finite Difference Method on Quadrilaterals -- Development and Application of Compatible Discretizations of Maxwell’s Equations En línea: http://dx.doi.org/10.1007/0-387-38034-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34840 Compatible Spatial Discretizations [documento electrónico] / SpringerLink (Online service) ; Douglas N. Arnold ; Pavel B. Bochev ; Richard B. Lehoucq ; Roy A. Nicolaides ; Shashkov, Mikhail . - New York, NY : Springer New York, 2006 . - XIV, 247 p : online resource. - (The IMA Volumes in Mathematics and its Applications, ISSN 0940-6573; 142) . ISBN : 978-0-387-38034-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Partial  differential  equations  Applied  mathematics  Engineering  Numerical  analysis  Applications  of  Differential  Equations  Analysis Clasificación: 51 Matemáticas Resumen: The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/ Nota de contenido: Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions -- Differential Complexes and Stability of Finite Element Methods I. The de Rham Complex -- Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex -- On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems -- Principles of Mimetic Discretizations of Differential Operators -- Compatible Discretizations for Eigenvalue Problems -- Conjugated Bubnov-Galerkin Infinite Element for Maxwell Equations -- Covolume Discretization of Differential Forms -- Mimetic Reconstruction of Vectors -- A Cell-Centered Finite Difference Method on Quadrilaterals -- Development and Application of Compatible Discretizations of Maxwell’s Equations En línea: http://dx.doi.org/10.1007/0-387-38034-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34840

Ejemplares

Signatura	Medio	Ubicación	Sub-localización	Sección	Estado
ningún ejemplar

Least-Squares Finite Element Methods / Max D. Gunzburger (2009)  

Público ISBD Título : Least-Squares Finite Element Methods Tipo de documento: documento electrónico Autores: Max D. Gunzburger ; SpringerLink (Online service) ; Pavel B. Bochev Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 166 Número de páginas: XXII, 660 p Il.: online resource ISBN/ISSN/DL: 978-0-387-68922-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Computer  mathematics  Numerical  Calculus  of  variations  Applied  Engineering  Fluid  mechanics  Appl.Mathematics/Computational  Methods  Computational  and  Variations  Optimal  Control;  Optimization  Dynamics Clasificación: 51 Matemáticas Resumen: The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engineers interested in either or both the theory and practice associated with the numerical solution of PDEs. The first part looks at strengths and weaknesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems. Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods. Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible discretizations for PDEs, multiphysics problems, and scientific computing. Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics. Nota de contenido: Survey of Variational Principles and Associated Finite Element Methods. -- Classical Variational Methods -- Alternative Variational Formulations -- Abstract Theory of Least-Squares Finite Element Methods -- Mathematical Foundations of Least-Squares Finite Element Methods -- The Agmon#x2013;Douglis#x2013;Nirenberg Setting for Least-Squares Finite Element Methods -- Least-Squares Finite Element Methods for Elliptic Problems -- Scalar Elliptic Equations -- Vector Elliptic Equations -- The Stokes Equations -- Least-Squares Finite Element Methods for Other Settings -- The Navier#x2013;Stokes Equations -- Parabolic Partial Differential Equations -- Hyperbolic Partial Differential Equations -- Control and Optimization Problems -- Variations on Least-Squares Finite Element Methods -- Supplementary Material -- Analysis Tools -- Compatible Finite Element Spaces -- Linear Operator Equations in Hilbert Spaces -- The Agmon#x2013;Douglis#x2013;Nirenberg Theory and Verifying its Assumptions En línea: http://dx.doi.org/10.1007/b13382 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33842 Least-Squares Finite Element Methods [documento electrónico] / Max D. Gunzburger ; SpringerLink (Online service) ; Pavel B. Bochev . - New York, NY : Springer New York, 2009 . - XXII, 660 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 166) . ISBN : 978-0-387-68922-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Computer  mathematics  Numerical  Calculus  of  variations  Applied  Engineering  Fluid  mechanics  Appl.Mathematics/Computational  Methods  Computational  and  Variations  Optimal  Control;  Optimization  Dynamics Clasificación: 51 Matemáticas Resumen: The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engineers interested in either or both the theory and practice associated with the numerical solution of PDEs. The first part looks at strengths and weaknesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems. Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods. Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible discretizations for PDEs, multiphysics problems, and scientific computing. Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics. Nota de contenido: Survey of Variational Principles and Associated Finite Element Methods. -- Classical Variational Methods -- Alternative Variational Formulations -- Abstract Theory of Least-Squares Finite Element Methods -- Mathematical Foundations of Least-Squares Finite Element Methods -- The Agmon#x2013;Douglis#x2013;Nirenberg Setting for Least-Squares Finite Element Methods -- Least-Squares Finite Element Methods for Elliptic Problems -- Scalar Elliptic Equations -- Vector Elliptic Equations -- The Stokes Equations -- Least-Squares Finite Element Methods for Other Settings -- The Navier#x2013;Stokes Equations -- Parabolic Partial Differential Equations -- Hyperbolic Partial Differential Equations -- Control and Optimization Problems -- Variations on Least-Squares Finite Element Methods -- Supplementary Material -- Analysis Tools -- Compatible Finite Element Spaces -- Linear Operator Equations in Hilbert Spaces -- The Agmon#x2013;Douglis#x2013;Nirenberg Theory and Verifying its Assumptions En línea: http://dx.doi.org/10.1007/b13382 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33842

Ejemplares

Signatura	Medio	Ubicación	Sub-localización	Sección	Estado
ningún ejemplar