Galerkin/Runge-Kutta Discretizations for Parabolic Partial Differential Equations PDF Download
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Author: Stephen Louis Keeling
Publisher:
ISBN:
Category : Differential equations, Parabolic
Languages : en
Pages : 652
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Book Description
Author: Stephen Louis Keeling
Publisher:
ISBN:
Category : Differential equations, Parabolic
Languages : en
Pages : 652
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Book Description
Author: Stephen L. Keeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
Author: Stephen Louis Keeling
Publisher:
ISBN:
Category : Galerkin methods
Languages : en
Pages : 36
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Book Description
Author: Stephen L. Keeling
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
Author: Vidar Thomee
Publisher: Springer Science & Business Media
ISBN: 3662033593
Category : Mathematics
Languages : en
Pages : 310
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Book Description
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Author: Jan G. Verwer
Publisher:
ISBN:
Category : Differential equations, Parabolic
Languages : en
Pages : 25
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Book Description
Abstract: "Numerical methods for parabolic PDEs have been studied for many years. A great deal of the research focuses on the stability problem in the time integration of the systems of ODEs which result from the spatial discretization. These systems often are stiff and highly expensive to solve due to a huge number of components, in particular for multi-space dimensional problems. The combination of stiffness and problem size has led to an interesting variety of special purpose time integration methods. In this paper we review such a class of methods, viz. explicit Runge-Kutta methods possessing extended real stability intervals."
Author: Jérôme Droniou
Publisher: Springer
ISBN: 3319790420
Category : Mathematics
Languages : en
Pages : 501
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Book Description
This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p
Author: Tilman Utz
Publisher:
ISBN: 9783844009323
Category :
Languages : en
Pages : 152
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Book Description
Author: Ulrich Langer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110548488
Category : Mathematics
Languages : en
Pages : 261
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Book Description
This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Author: Nikolai Bakaev
Publisher: Elsevier
ISBN: 0080462081
Category : Mathematics
Languages : en
Pages : 303
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Book Description
This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods. Key features: * Presents a unified approach to examining discretization methods for parabolic equations. * Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. * Deals with both autonomous and non-autonomous equations as well as with equations with memory. * Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods. * Provides comments of results and historical remarks after each chapter. · Presents a unified approach to examining discretization methods for parabolic equations. · Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. · Deals with both autonomous and non-autonomous equations as well as with equations with memory. · Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail. ·Provides comments of results and historical remarks after each chapter.
