Penalized and Immersed Finite Element Method for Interface Problems

About the Project

This research develops novel Penalized (PFEM) and Immersed Finite Element Methods (IFEM) to solve interface problems where material properties change abruptly, such as in fluid-structure interactions or composite materials. Unlike traditional methods requiring complex mesh alignment, PFEM/IFEM use penalty terms or adaptive basis functions to efficiently capture discontinuities. The project will establish mathematical foundations for these methods, enhance their stability for moving interfaces (e.g., biomedical flows), and validate performance against conventional approaches. By eliminating mesh-fitting constraints, this work will enable more accurate and cost-effective simulations for applications in biomechanics, materials science, and environmental engineering.

For more information about doctoral scholarship and PhD programme at Xi’an Jiaotong-Liverpool University (XJTLU), please visit:

• https://www.xjtlu.edu.cn/en/admissions/global/entry-requirements/
• https://www.xjtlu.edu.cn/en/admissions/global/fees-and-scholarship

Supervisors:

• Principal supervisor: Professor/Dr Jie Chen (XJTLU)
• Co-supervisor: Professor/Dr Fei Ma (XJTLU)
• Co-supervisor: Professor/Dr Linglong Yuan (UoL)

Requirements:

A Master's degree with Merit and a Bachelor's degree with first-class or upper second-class honors are required for PhD admissions. Exceptional candidates holding only a Bachelor's degree may be considered on an individual basis in certain disciplines.

Evidence of good spoken and written English is essential. The candidate should have an IELTS (or equivalent) score of 6.5 or above, if the first language is not English. This position is open to all qualified candidates irrespective of nationality.

Degree:

The student will be awarded a PhD degree from the University of Liverpool (UK) upon successful completion of the program.

Funding:

The PhD studentship is available for three years subject to satisfactory progress by the student. The award covers tuition fees for three years (currently equivalent to RMB 99,000 per annum). It also provides up to RMB 16,500 to allow participation at international conferences during the period of the award. The scholarship holders are expected to conduct the majority of their research at XJTLU in Suzhou, China. However, they may apply for a short-term research visit to the University of Liverpool if the project requires it.

How to Apply:

Interested applicants are advised to email jie.chen01@xjtlu.edu.cn the following documents for initial review and assessment (please put the project title in the subject line).

• CV
• Two formal reference letters
• Personal statement outlining your interest in the position
• Certificates of English language qualifications (IELTS or equivalent)
• Full academic transcripts in both Chinese and English (for international students, only the English version is required)
• Verified certificates of education qualifications in both Chinese and English (for international students, only the English version is required)
• PDF copy of Master Degree dissertation (or an equivalent writing sample) and examiners reports available

Contact:

Please email jie.chen01@xjtlu.edu.cn with a subject line of the PhD project title.

The principal supervisor’s profile is linked here:

https://scholar.xjtlu.edu.cn/en/persons/JieChen01