CEE Seminar - Professor Paolo Zunino, Univrsity of Pittsburgh, Mechanical Engineering and Materials Science
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June 6, 2014 - 12:00pm to 1:00pm
CEE Seminar, Professor Paolo Zunino, Dept. of mechanical Engineering and Materials Science, University of Pittsburgh. http://www.engineering.pitt.edu/ProfessionalProfile.aspx?id=2147504147 Seminar Title: XFEM DISCRETIZATION AND ANALYSIS OF STEADY AND TIME DEPENDENT CONTRAST PROBLEMS Abstract Numerical experiments performed by several authors repeatedly confirmed that the extended finite element method (XFEM) combined with classical time stepping schemes, such as backward Euler or Crank-Nicolson, provides optimal rates of convergence when applied to problems with moving interfaces . In spite of the rapid spread of this discretization approach, a complete theory for the XFEM approximation of time dependent problems is not available yet. The objective of this work is to discuss a space and time error analysis of different variants of XFEM combined with the backward Euler time advancing scheme when applied to problems with moving interfaces . Our results prove that the discretization error, measured in the natural norms, decreases with the expected rate, when space and time discretization steps are refined. High order approximation schemes in time could be also analyzed within the theoretical framework proposed here. Numerical experiments are addressed, to support the theoretical results and to verify the implementation of the algorithms.....