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Higher Order FE Methods for Challenging Problems in Science and Engineering

Leszek Demkowicz, University of Texas-Austin

Jay Gopolakrishnan, Portland State University

High  order  discretization  methods  offer  higher  convergence  rates  and  potentially  superior quality  of numerical  solutions.  The  benefits,  however,  are  conditional  on  resolving  several challenging  issues,  to mention a few:
•discrete stability,
•complexity of data structures,
•construction of high order shape functions,
•complexity of postprocessing,
•a-posteriori error estimation and adaptivity.
We are seeking the participation of colleagues who work on high order Finite Element methods in context of difficult applications. The discretization methodologies may include standard conforming methods as well as DG, hybrid DG, least squares and DPG methods.  We are interested in both linear and nonlinear applications with an emphasis on multiphysics problems requiring couplings of different elements.