23 citations · 37 across the 15 of their papers we have counts for
5 papers · 1 filter
Shape optimisation for adaptive -refinement: the one-dimensional case with residual based error estimators
Philip J. Herbert
We consider -refinement for the finite element discretisation of a Poisson problem. The goal of -refinement is to reposition the nodes of a computational mesh in order to bet…
Finite element approximation of the enthalpy formulation for Stefan problems on evolving surfaces
Philip J. Herbert, Thomas Sales, Chandrasekhar Venkataraman
We propose, and analyse, a spatially discrete evolving surface finite element method for the approximation of the enthalpy formulation of the two-phase Stefan problem posed on an e…
Finite element approximation to the non-stationary quasi-geostrophic equation
Dohyun Kim, Amiya K. Pani, Eun-Jae Park
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation m…
The Stochastic Steepest Descent Method for Robust Optimization in Banach Spaces
Neil K. Chada, Philip J. Herbert
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approxima…
Second order splitting of a class of fourth order PDEs with point constraints
Charles M. Elliott, Philip J. Herbert
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a…