Leszek Demkowicz's Books

Mathematical Theory of Finite Elements

By: Leszek F. Demkowicz

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Mathematical Theory of Finite Elements

By: Leszek F. Demkowicz

This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.

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Page Count

217

Publisher

SIAM

Published Date

ISBN 10

1611977738

ISBN 13

9781611977738

Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

By: Leszek Demkowicz

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Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

By: Leszek Demkowicz

Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementat

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Page Count

428

Publisher

CRC Press

Published Date

ISBN 10

1420011685

ISBN 13

9781420011685

Applied Functional Analysis

By: J. Tinsley Oden,Leszek Demkowicz

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Applied Functional Analysis

By: J. Tinsley Oden,Leszek Demkowicz

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject. It motivates students to study functional analysis by providing many contemporary applications and examples drawn from mechanics and science. This well-received textbook starts with a thorough introduction to modern mathematics before continuing with detailed coverage of linear algebra, Lebesque measure and integration theory, plus topology with metric spaces. The final two chapters provides readers with an in-depth look at the theory of Banach and Hilbert spaces before concluding with a brief introduction to Spectral Theory. The Third Edition is more accessible and promotes interest and motivation among students to prepare them for studying the mathematical aspects of numerical analysis and the mathematical theory of finite elements.

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601

Publisher

CRC Press

Published Date

ISBN 10

1498761151

ISBN 13

9781498761154

Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

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Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

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Page Count

254

Publisher

Springer

Published Date

ISBN 10

3540783199

ISBN 13

9783540783190

Applied Functional Analysis

By: J. Tinsley Oden,Leszek Demkowicz

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Applied Functional Analysis

By: J. Tinsley Oden,Leszek Demkowicz

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Page Count

601

Publisher

CRC Press

Published Date

ISBN 10

1498761151

ISBN 13

9781498761154

Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

By: Leszek Demkowicz

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Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

By: Leszek Demkowicz

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Page Count

428

Publisher

CRC Press

Published Date

ISBN 10

1420011685

ISBN 13

9781420011685

Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications

By: Leszek Demkowicz,Jason Kurtz,David Pardo,Maciek Paszenski,Waldemar Rachowicz,Adam Zdunek

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Computing with hp-ADAPTIVE FINITE ELEMENTS

Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications

By: Leszek Demkowicz,Jason Kurtz,David Pardo,Maciek Paszenski,Waldemar Rachowicz,Adam Zdunek

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the

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Page Count

437

Publisher

CRC Press

Published Date

ISBN 10

1420011693

ISBN 13

9781420011692

Applied Functional Analysis, Second Edition

By: J. Tinsley Oden,Leszek Demkowicz

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Applied Functional Analysis, Second Edition

By: J. Tinsley Oden,Leszek Demkowicz

Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods. While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources. New to the Second Edition Completely revised section on lim sup and lim inf New discussions of connected sets, probability, Bayesian statistical inference, and the generalized (integral) Minkowski inequality New sections on elements of multilinear algebra and determinants, the singular value decomposition theorem, the Cauchy principal value, and Hadamard finite part integrals New example of a Lebesgue non-measurable set Ideal for a two-semester course, this proven textbook teaches students how to prove theorems and prepares them for further study of more advanced mathematical topics. It helps them succeed in formulating research questions in a mathematically rigorous way.

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Page Count

589

Publisher

CRC Press

Published Date

ISBN 10

1420091956

ISBN 13

9781420091953

Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

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Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

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Page Count

244

Publisher

Springer

Published Date

ISBN 10

3540847634

ISBN 13

9783540847632

Book's by Leszek Demkowicz

Mathematical Theory of Finite Elements

Mathematical Theory of Finite Elements

Computing with hp-ADAPTIVE FINITE ELEMENTS

Computing with hp-ADAPTIVE FINITE ELEMENTS

Applied Functional Analysis

Applied Functional Analysis

Mixed Finite Elements, Compatibility Conditions, and Applications

Mixed Finite Elements, Compatibility Conditions, and Applications

Applied Functional Analysis

Applied Functional Analysis

Computing with hp-ADAPTIVE FINITE ELEMENTS

Computing with hp-ADAPTIVE FINITE ELEMENTS

Computing with hp-ADAPTIVE FINITE ELEMENTS

Computing with hp-ADAPTIVE FINITE ELEMENTS

Applied Functional Analysis, Second Edition

Applied Functional Analysis, Second Edition

Mixed Finite Elements, Compatibility Conditions, and Applications

Mixed Finite Elements, Compatibility Conditions, and Applications

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