LEADER 04386nam 2200685 450 001 996466550503316 005 20231110225722.0 010 $a3-030-61803-X 035 $a(CKB)4100000011801696 035 $a(MiAaPQ)EBC6522070 035 $a(Au-PeEL)EBL6522070 035 $a(OCoLC)1243542810 035 $a(PPN)254721710 035 $a(EXLCZ)994100000011801696 100 $a20211012d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aFractals in engineering $etheoretical aspects and numerical approximations /$fedited by Maria Rosaria Lancia and Anna Rozanova-Pierrat 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (179 pages) $cillustrations 225 1 $aSEMA SIMAI Springer ;$vv.8 311 $a3-030-61802-1 327 $aIntro -- 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. 327 $aGeneralization of Rellich-Kondrachov Theorem and Trace Compactness for Fractal Boundaries -- 1 Introduction -- 2 Sobolev Extension Domains -- 3 Trace on the Boundary and Green Formulas -- 3.1 Framework of d-Sets and Markov's Local Inequality -- 3.2 General Framework of Closed Subsets of Rn -- 3.3 Integration by Parts and the Green Formula -- 4 Sobolev Admissible Domains and the Generalization of the Rellich-Kondrachov Theorem -- 5 Compactness of the Trace -- 6 Application to the Poisson Boundary Valued and Spectral Problems -- References. 410 0$aSEMA SIMAI Springer 606 $aCalculus 606 $aApplied mathematics 606 $aFunctions 606 $aHarmonic analysis 606 $aMathematical analysis 606 $aCàlcul$2thub 606 $aMatemàtica aplicada$2thub 606 $aFuncions$2thub 606 $aAnàlisi harmònica$2thub 606 $aAnàlisi matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aCalculus. 615 0$aApplied mathematics. 615 0$aFunctions. 615 0$aHarmonic analysis. 615 0$aMathematical analysis. 615 7$aCàlcul 615 7$aMatemàtica aplicada 615 7$aFuncions 615 7$aAnàlisi harmònica 615 7$aAnàlisi matemàtica 676 $a658.4034 702 $aLancia$b Maria Rosaria 702 $aAnna Rozanova-Pierrat 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466550503316 996 $aFractals in engineering$91897492 997 $aUNISA