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math.NA2021
Additive Schwarz methods for serendipity elements
Jorge Marchena-Menendez, Robert C. Kirby
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensor-prod…
math.NA2020
Irksome: Automating Runge--Kutta time-stepping for finite element methods
Patrick E. Farrell, Robert C. Kirby, Jorge Marchena-Menendez
While implicit Runge--Kutta methods possess high order accuracy and important stability properties, implementation difficulties and the high expense of solving the coupled algebrai…