A New Family of Conforming Finite Elements on Cubical Meshes

The wide ranging zoo of conforming finite element methods is partially categorized into four columns' of element types by the Periodic Table of Finite Elements. Within these columns lie various kinds of elements that are both well-known and widely used to compute numerical approximations of solutions to partial differential equations. In this talk, I will present afifth column' of elements for the table that fits naturally within the mathematical structures encoded in the table while promising substantial computational savings for methods on large meshes of squares or cubes. The talk is meant to be accessible to a wide audience and will begin with a discussion of the potential benefit of the new elements to subsurface flow modeling as well as other applications. This is joint work with Tyler Kloefkorn.