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Calculus. --- Functional analysis. --- Functions. --- Harmonic analysis. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential equations --- Numbers, Complex --- Set theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Mètode dels elements finits --- Equacions en derivades parcials --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Karman --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica) --- Anàlisi numèrica --- Equacions de Von Kármán
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Calculus. --- Functional analysis. --- Functions. --- Harmonic analysis. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential equations --- Numbers, Complex --- Set theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Mètode dels elements finits --- Equacions en derivades parcials --- Anàlisi funcional --- Mètodes de Galerkin --- Mètodes de Sinc --- Mètodes de Sinc-Galerkin --- Anàlisi numèrica --- Càlcul funcional --- Càlcul de variacions --- Àlgebres de Hilbert --- Àlgebres topològiques --- Anàlisi funcional no lineal --- Anàlisi microlocal --- Espais analítics --- Espais de Hardy --- Espais d'Orlicz --- Espais funcionals --- Espais vectorials normats --- Espais vectorials --- Filtres digitals (Matemàtica) --- Funcionals --- Funcions vectorials --- Multiplicadors (Anàlisi matemàtica) --- Pertorbació (Matemàtica) --- Teoria d'operadors --- Teoria de distribucions (Anàlisi funcional) --- Teoria de functors --- Teoria de l'aproximació --- Teoria del funcional de densitat --- Teoria espectral (Matemàtica) --- Equacions funcionals --- Equacions integrals --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Karman --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Equacions de Von Kármán
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This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.
Functional analysis --- Differential equations --- differentiaalvergelijkingen --- functies (wiskunde)
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Elasticitat --- Models matemàtics --- Física de l'estat sòlid --- Física --- Dinàmica reticular --- Electrònica de l'estat sòlid --- Estructura cristal·lina (Sòlids) --- Micromecànica --- Vidres de spin --- Sòlids --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Estàtica --- Física matemàtica --- Impacte --- Mecànica --- Mecànica analítica --- Propietats de la matèria --- Aeroelasticitat --- Equacions de Von Karman --- Fotoelasticitat --- Histèresi --- Mecànica dels medis continus --- Ones elàstiques --- Termoelasticitat --- Plasticitat --- Viscoelasticitat --- Esforç i tensió --- Reologia --- Resistència de materials --- Equacions de Von Kármán --- Elasticity. --- Diffusion --- Solid state physics. --- Mathematical models. --- Physics --- Solids --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Elastic properties --- Young's modulus --- Properties
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This book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.
Numerical analysis --- Solid state physics --- Applied physical engineering --- Computer science --- Computer. Automation --- toegepaste mechanica --- informatica --- software engineering --- informaticaonderzoek --- mechanica --- numerieke analyse
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Functional analysis --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde
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Functional analysis --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde
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Functional analysis --- Differential equations --- differentiaalvergelijkingen --- functies (wiskunde)
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Numerical analysis --- Solid state physics --- Applied physical engineering --- Computer science --- Computer. Automation --- toegepaste mechanica --- informatica --- software engineering --- informaticaonderzoek --- mechanica --- numerieke analyse
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