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…
Small deformations of a near cylindrical tube for the Canham-Helfrich Energy with applications to biological membranes
Charles M. Elliott, Carsten Gräser, Philip J. Herbert
In this article we develop a quadratic energy which approximates the Canham-Helfrich energy for a tube-like surface with clamped boundary and area constraint. The energy is suited…
Combining diffuse and sharp interface methods in shape optimisation
Philip J. Herbert, Michael Hinze, Christian Kahle
We develop a concept for the numerical treatment of shape optimization problems based on the combination of phase field and sharp interface methods. On the one hand, phase field me…
Global convergence of -steepest descent for PDE constrained shape optimisation with semilinear elliptic equations in function space
Klaus Deckelnick, Philip J. Herbert, Michael Hinze
We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is rea…