Evan S. Gawlik

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We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times(More)
With an environment comparable to that of primordial Earth, a surface strewn with liquid hydrocarbon lakes, and an atmosphere denser than that of any other moon in the solar system, Saturn's largest moon Titan is a treasure trove of potential scientific discovery and is the target of a proposed NASA mission scheduled for launch in roughly one decade. A(More)
In this paper we develop and test a structure-preserving discretiza-tion scheme for rotating and/or stratified fluid dynamics. The numerical scheme is based on a finite dimensional approximation of the group of volume preserving diffeomorphisms recently proposed in [25, 9] and is derived via a discrete version of the Euler-Poincaré variational formulation(More)
We present a unified analysis of finite element methods for problems with prescribed moving boundaries. In particular, we study an abstract parabolic problem posed on a moving domain with prescribed evolution, discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times. The moving mesh is(More)
We construct interpolation operators for functions taking values in a symmetric space – a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition – a(More)
We derive upper bounds on the difference between the orthogonal projections of a smooth function u onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the spaces is contained in a common region whose measure tends to zero under mesh refinement. The bounds apply, in(More)
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