13 citations · 37 across the 12 of their papers we have counts for
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math.NA2016
Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface
Klaus Deckelnick, Vanessa Styles
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a leve…
math.NA2016
Numerical Analysis for a System Coupling Curve Evolution to Reaction-Diffusion on the Curve
John W. Barrett, Klaus Deckelnick, Vanessa Styles
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equatio…
math.OC2016★ 10 cited
A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws
F. Yang, C. Venkataraman, V. Styles +1
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal con…