The Finite Element Method for Initial Value Problems

Karan S. Surana attended undergraduate school at Birla Institute of Technology and Science (BITS), Pilani, India and received a B.E. in mechanical engineering in 1965. He then attended the University of Wisconsin, Madison where he obtained M.S. and Ph.D. in mechanical engineering in 1967 and 1970. He joined The University of Kansas, Department of Mechanical Engineering faculty where he is currently serving as Deane E. Ackers University Distinguished Professor of Mechanical Engineering. His areas of interest and expertise are computational mathematics, computational mechanics, and continuum mechanics. He is the author of over 350 research reports, conference papers, and journal papers. J. N. Reddy is a Distinguished Professor, Regents’ Professor, and inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas. Dr. Reddy earned a Ph.D. in Engineering Mechanics in 1974 from University of Alabama in Huntsville. He worked as a Post-Doctoral Fellow in Texas Institute for Computational Mechanics (TICOM) at the University of Texas at Austin, Research Scientist for Lockheed Missiles and Space Company, Huntsville, during l974- 75, and taught at the University of Oklahoma from 1975 to 1980, Virginia Polytechnic Institute & State University from 1980 to 1992, and at Texas A&M University from 1992. Professor Reddy also played active roles in professional societies as the President of USACM, founding member of the General Council of IACM, Secretary of Fellows of AAM, member of the Board of Governors of SES, Chair of the Engineering Mechanics Executive Committee, among several others. He either served or currently serving on the editorial boards of a large number of journals. In addition, he served as the Editor of Applied Mechanics Reviews, Mechanics of Advanced Materials and Structures, the International Journal of Computational Methods in Engineering Science and Mechanics, and the International Journal of Structural Stability and Dynamics.

Introduction. Concepts from Functional Analysis and Calculus of Variations. Space-Time Coupled Classical Methods of Approximation. Space-Time Finite Element Method. Space-Time Decoupled or Quasi Finite Element Methods. Methods of Approximation for ODEs in Time. Finite Element for ODEs in Time. Stability Analysis of the Methods of Approximation. Mode Superposition Technique. Errors in Numerical Solutions of Initial Value Problems. Appendix A: Nondimensionalizing Mathematical Models. Appendix B: Mapping and Interpolation Theory. Appendix C: Numerical Integration using Gauss Quadrature. Index