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PhD Studentship on Numerical Analysis of a Stochastic Phase Interface Model for Application in Lithium Ion Batteries

University of Sussex

Qualification Type: PhD
Location: Falmer
Funding for: UK Students, EU Students
Funding amount: Covers fees and living expenses
Hours: Full Time
Placed On: 13th June 2019
Closes: 31st August 2019


A three and a half year studentship for a UK or EU student which covers fees and living expenses.


This studentship centres on the analysis and numerical simulation of mathematical models for cracking and fracturing of electrodes in Lithium-ion batteries.

We will address two models.

Model 1 will take the form of a (deterministic) coupled system of partial differential equations.

Model 2 will include the addition of stochastic effects modelling battery user behaviour in a statistical sense. 


You will receive:

  • Fully-funded tuition fees for 3.5 years at the UK/EU rate only.
  • A tax-free bursary for living costs at £15009 per year (2019-20).
  • An additional fund of £1650 per year for conference attendance and additional training.

PhD project

Model 1 will comprise (i) a degenerate fourth-order Cahn–Hilliard type variational inequality, (ii) the linear elasticity equations, and (iii) a degenerate Ginzburg–Landau variational inequality.

Model 2 will include the addition of stochastic effects modelling the battery user behaviour in a statistical sense. The effects will enter the partial differential equations (which then become stochastic partial differential equations) in the form of noise in the boundary, initial or forcing-term data. We will discretise both models using adaptive finite element approximations and the resulting approximations will be analysed and then solved using the adaptive finite element tool box ALBERTA and we will also explore other FEM libraries such as Fenics-Dolfin, Firedrake and Deal.II.

Specific problems

  • derive and implement a fully practical finite element approximation of the system;
  • analyse the resulting finite element approximation; proving existence, stability bounds, convergence results, error estimates;
  • consider a posteriori error analysis and the associated adaptive methodology based on recent advances in this field to derive efficient methods;
  • extend the system to include stochastic effects and derive, implement and analyse finite element approximations of this extended stochastic system.

For more information, see:

2) D. Braess (2007). Finite Elements, Cambridge University Press.


You must be

  • A UK or European Union (EU) student. Funding restrictions limit availability beyond the EU & UK.
  • Have, or expect to have a good UK Bachelor/Master’s degree (or non-UK equivalent qualification) in Mathematics or a closely-related subject.
  • Meet the English language requirements (see entry requirements) 

How to apply

Apply through the Sussex on-line postgraduate application system:

In the Other Information/Funding Section state that you are applying for this studentship.

Send an email to Dr Lakkis and Prof Styles to confirm you have applied.

Contact us

Informal enquiries are welcome and should be directed to

Dr Omar Lakkis ( ) and

Prof Vanessa Styles ( ).


Students are encouraged to apply, or at least send an expression of interest, as early as possible. The studentship will be filled as soon as a suitable candidate can be found.

Possible start dates are 23 September 2019, 27 January 2020, or 11 May 2020.

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