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Non-uniqueness of Solutions to the Conformal Formulation
Michael Holst, Caleb Meier
It is well-known that solutions to the conformal formulation of the Einstein constraint equations are unique in the cases of constant mean curvature (CMC) and near constant mean cu…
Convergence of Goal-Oriented Adaptive Finite Element Methods for Semilinear Problems
Michael Holst, Sara Pollock, Yunrong Zhu
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly…
Two-Grid Methods for Semilinear Interface Problems
Michael Holst, Ryan Szypowski, Yunrong Zhu
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the ta…
Finite Element Exterior Calculus for Evolution Problems
Andrew Gillette, Michael Holst, Yunrong Zhu
Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most com…