Lecturer: Sergey KOROTOV, BCAM, Bilbao, Basque Country, Spain Webpages: http://www.bcamath.org/en/people/korotov Title: AN INTRODUCTION TO THE FINITE ELEMENT METHOD Date and time: Mon, May 27 to Fri, May 31 2013, 9:00 to 11:00 Abstract: This course will be devoted to several topics under current active research in the finite element (FE) analysis. Inspite the fact that the FEM theory was quite well established already three decades ago, appearing new applications and fast growing capabilities of modern computers permanently force practitioners and researchers to look again and again at various (practical and theoterical) aspects of this powerful computational technique, especially at those associated with 3 (and higher-dimensional) problems. Program: 1. Basic ideas of FEM. FEM Terminology. Historical remarks. Applications. 2. Convergence and superconvcergence results. 3. A posteriori error estimation techniques. 4. Discrete maximum principles. 5. On FE mesh generation and adaptivity. Open problems. Bibliography: [[1] O. Axelsson, V.A. Barker. "Finite Element Solution of Boundary Value Problems. Theory and Computation", Academic Press, London, 1984. [2] P. G. Ciarlet. "The finite element method for elliptic problems", North-Holland Amsterdam, 1978. [3] M. Krizek, P. Neittaanmaki. "Mathematical and Numerical Modelling in Electrical Engineering: Theory and Applications", Kluwer, Dordrecht, 1996. [4] P. Neittaanmaki, S. Repin. "Reliable Methods for Computer Simulation: Error Control and A Posteriori Estimates", Elsevier, 2004. [5] V. Thomee. "Galerkin Finite Element Methods for Parabolic Problems", Springer Series in Computational Mathematics, vol. 25, Springer-Verlag, Berlin Heidelberg, 2006. [6] L. B. Wahlbin. "Superconvergence in Galerkin Finite Element Methods", Springer, 1995.