Lecture Notes

• Primer of Adaptive Finite Element Methods, (with A. Veeser)
  Multiscale and Adaptivity: Modeling, Numerics and Applications, CIME Lectures, eds R. Naldi and G. Russo, Springer (to appear).
• Cime Lectures



• Optimal Multilevel Methods for H(grad), H(curl), and H(div) Systems on Graded and Unstructured Grids, (with J. Xu and L. Chen)
  Multiscale, Nonlinear and Adaptive Approximation, R. DeVore and A. Kunoth eds, Springer (2009), 599-659.
• Multilevel Methods



• Theory of Adaptive Finite Element Methods: an Introduction , (with K.G. Siebert and A. Veeser)
  Multiscale, Nonlinear and Adaptive Approximation, R. DeVore and A. Kunoth eds, Springer (2009), 409-542.
• AFEM



• Adaptive Finite Element Methods for Elliptic PDE, 2006 CNA Summer School, Probabilistic and Analytical Perpectives in Contemporary PDE.
  
  • Lecture 1. The Finite Element Method: Properties and Error Analysis
  • Lecture 2. Adaptivity I: Design and Convergence of AFEM
  • Lecture 3. Adaptivity II: General Operators and Extensions
  • Lecture 4. Complexity of AFEM
  • Lecture 5. Pointwise Error Control and Applications