Fractals in engineering : theoretical aspects and numerical approximations / / edited by Maria Rosaria Lancia and Anna Rozanova-Pierrat

• Record Nr.: UNINA9910484636403321
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-61803-X
• Descrizione fisica: 1 online resource (179 pages) : illustrations
• Collana: SEMA SIMAI Springer ; ; v.8
• Disciplina: 658.4034
• Soggetti: Calculus; Applied mathematics; Functions; Harmonic analysis; Mathematical analysis; Càlcul; Matemàtica aplicada; Funcions; Anàlisi harmònica; Anàlisi matemàtica; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- A Numerical Approach to a Nonlinear Diffusion Model for Self-Organized Criticality Phenomena -- 1 Introduction -- 2 The Basic Model -- 3 Numerical Approximation on a Fixed Grid -- 4 Approximation on a Synchronized Family of Grids -- 5 Numerical Tests -- References -- Approximation of 3D Stokes Flows in Fractal Domains -- 1 Introduction -- 2 Preliminaries -- 3 Existence and Uniqueness Results -- 4 Regularity in Weighted Sobolev Spaces -- 5 Mean Shear Stress -- 6 Numerical Approximation -- 7 Numerical Simulations -- References -- ∞-Laplacian Obstacle Problems in Fractal ; Domains -- 1 Introduction -- 2 Fractal Domains, Approximating Domains and Fibers -- 3 Setting and Asymptotic Behavior -- 4 Uniqueness and Perspectives -- 5 Uniform and Error Estimates -- References -- Discretization of the Koch Snowflake Domain with Boundary and Interior Energies -- 1 Introduction -- 2 Dirichlet Form on the Koch Snowflake -- 3 Dirichlet Form on the Snowflake Domain -- 4 Inductive Mesh Construction and Discrete Energy Forms -- 5 Numerical Results -- 5.1 Algorithm and Implementation -- 5.2 The Eigenvalue Counting Function -- 5.3 Eigenvectors and Eigenvalues in the Low Eigenvalue Regime -- 5.4 Localization in the High Eigenvalue Regime -- 6 A Landscape Approach to High Frequency Localization -- References -- On the Dimension of the Sierpinski Gasket in l2 -- 1 Introduction -- 2 Invariant Sets -- 2.1 Infinite Dimensional Sierpinski Gasket -- 2.2 Hausdorff Dimension of Invariant Sets -- 2.3 N-Dimensional Simplices -- 3 Invariant Measures -- References -- On the External Approximation of Sobolev Spaces by M-Convergence -- 1 Introduction -- 2 Sobolev Space Approximations -- 3 The M-Convergence Result -- 4 Proof of Lemma 1 -- 5 Proof of Lemma 2 -- 6 Comments -- References.; Generalization of Rellich-Kondrachov Theorem and Trace Compactness for Fractal Boundaries -- 1 Introduction -- 2 Sobolev Extension Domains -- 3 Trace on the Boundary and Green Formulas -- 3.1 Framework of d-Sets and Markov's Local Inequality -- 3.2 General Framework of Closed Subsets of Rn -- 3.3 Integration by Parts and the Green Formula -- 4 Sobolev Admissible Domains and the Generalization of the Rellich-Kondrachov Theorem -- 5 Compactness of the Trace -- 6 Application to the Poisson Boundary Valued and Spectral Problems -- References.