Analysis and Numerics of Partial Differential Equations (eBook)

Part I A Historical Perspective.- Personal Memories.- Some Aspects of the Research of Enrico Magenes in Partial Differential Equations.- Enrico Magenes and the Dam Problem.- Inverse Problems in Electrocardiology.- Stefan Problems and Numerical Analysis.- Enrico Magenes and the Teaching of Mathematics.- List of Mathematical Works Authored or Edited by Enrico Magenes.- Part II Recent Developments.- Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case.- Spaces of Finite Element Differential Forms.- A Priori Bounds for Solutions of a Nonlocal Evolution PDE.- On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems.- A Theory and Challenges for Coarsening in Microstructure.- A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation.- Analysis and Numerics of Some Fractal Boundary Value Problems.- AFEM for Geometric PDE: The Laplace-Beltrami Operator.- Generalized Reduced Basis Methods and n-Width Estimates for the Approximation of the Solution Manifold of Parametric PDEs.- Variational Formulation of Phase Transitions with Glass Formation.