Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Low Order Finite Element Method for Poroelasticity with Applications
  to Lung Modelling   In this thesis we develop a stabilised finite element method for solving the
equations of poroelasticity to enable solving complex models of biological
tissues such as the human lungs. For the proposed numerical scheme, we use the
lowest possible approximation order: piecewise constant approximation for the
pressure, and piecewise linear continuous elements for the displacements and
fluid flux. Due to the discontinuous pressure approximation, sharp pressure
gradients due to changes in material coefficients or boundary layer solutions
can be captured reliably. We begin by developing theoretical results for
approximating the linear poroelastic equations valid in small deformations. In
particular, we prove existence and uniqueness, an energy estimate and an
optimal a-priori error estimate for the discretised problem. We then extend
this work and construct a stabilised finite element method to solve the
poroelastic equations valid in large deformations. We present the linearisation
and discretisation for this nonlinear problem, and give a detailed account of
the implementation. We rigorously test both the linear and nonlinear finite
element method using numerous test problems to verify theoretical stability and
convergence results, and the method's ability to reliably capture steep
pressure gradients. Finally, we derive a poroelastic model for lung parenchyma
coupled to an airway fluid network model, and develop a stable method to solve
the coupled model. Numerical simulations, on a realistic lung geometry,
illustrate the coupling between the poroelastic medium and the network flow
model, and simulations of tidal breathing are shown to reproduce global
physiologically realistic measurements. We also investigate the effect of
airway constriction and tissue weakening on the ventilation, tissue stress and
alveolar pressure distribution.

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The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph