P. J. Herbert

activity

20192026

W^{1, \infty}

approach to shape optimisation with Lipschitz domains

23 citations · 37 across the 15 of their papers we have counts for

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math.NA2026

Shape optimisation for adaptive $r$ -refinement: the one-dimensional case with residual based error estimators

Philip J. Herbert

We consider $r$ -refinement for the finite element discretisation of a Poisson problem. The goal of $r$ -refinement is to reposition the nodes of a computational mesh in order to bet…

math.NA2026

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…

Shape optimisation for adaptive r-refinement: the one-dimensional case with residual based error estimators

Finite element approximation of the enthalpy formulation for Stefan problems on evolving surfaces

Shape optimisation for adaptive $r$ -refinement: the one-dimensional case with residual based error estimators