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The Cutting and Floating Method for Paraffin-embedded Tissue for Sectioning
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A cut finite element method for elliptic bulk problems with embedded surfaces.

Erik Burman1, Peter Hansbo2, Mats G Larson3

  • 11Mathematics, University College London, London, UK.

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|March 16, 2019
PubMed
Summary
This summary is machine-generated.

We developed a new finite element method for simulating fluid flow in fractured porous media. This approach accurately models flow across fractures, improving predictions for complex geological systems.

Keywords:
EmbeddedFinite elementFracturesUnfitted

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Area of Science:

  • Computational fluid dynamics
  • Geosciences
  • Numerical analysis

Background:

  • Simulating fluid flow in fractured porous media is crucial for understanding subsurface processes.
  • Existing methods often struggle with accurately capturing the complex interactions at fracture interfaces.
  • Developing robust numerical techniques is essential for reliable subsurface flow modeling.

Purpose of the Study:

  • To introduce an unfitted finite element method for modeling flow in fractured porous media.
  • To accurately represent the coupling and jumps in solution gradients across fractures.
  • To provide a framework for simulating flow in both simple and bifurcating fracture networks.

Main Methods:

  • Utilizing an unfitted finite element method with Nitsche-type mortaring for fracture coupling.
  • Modeling the fracture flow field using averaged traces of bulk variables.
  • Incorporating the Laplace-Beltrami operator for fracture transport via averaged gradient projections.
  • Proving optimal order error estimates under regularity assumptions.

Main Results:

  • The proposed method accurately represents the jump in the normal component of the gradient across fractures.
  • Simultaneous modeling of bulk and fracture flow fields is achieved.
  • The method is shown to be effective through numerical examples, including bifurcating fractures.

Conclusions:

  • The unfitted finite element method provides an accurate and robust approach for flow in fractured porous media.
  • The Nitsche-type mortaring effectively handles fracture coupling.
  • The method shows promise for applications in various subsurface flow simulations.