Graduate Thesis Or Dissertation
 

Numerical Analysis of a System of Parabolic Variational Inequalities with Application to Biofilm Growth

Public Deposited

Downloadable Content

Download PDF
https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ks65hk08s

Descriptions

Attribute NameValues
Creator
Abstract
  • In this work we consider a mathematical and computational model for biofilm growth and nutrient utilization. In particular, we are interested in a model appropriate at a scale of interface. The model is a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs). One of these PDEs is subject to a constraint, which can be characterized as a parabolic variational inequality (PVI). Solutions to PVI have low regularity which limits the numerical scheme to low order. We analyze the numerical approximations of this model by implementing two numerical methods: (i) low order Galerkin finite element method, and (ii) mixed finite element method with the lowest order Raviart-Thomas elements. We show the well-posedness of the approximate problems, derive rigorous error estimates, and present numerical experiments in 1D, 2D, and 3D that confirm the predicted estimates. We also illustrate the behavior of biofilm and nutrient dynamics in simple and in complex porescale geometries.
License
Resource Type
Date Issued
Degree Level
Degree Name
Degree Field
Degree Grantor
Commencement Year
Advisor
Committee Member
Academic Affiliation
Rights Statement
Publisher
Peer Reviewed
Language

Relationships

Parents:

This work has no parents.

In Collection:

Items

Thumbnail Title Date Uploaded Visibility Actions
file details AlhammaliAzharS2019.pdf 2019-06-08 Public Download