Convergence Analysis of Discontinuous Galerkin Methods for Poroelasticity Equations
| dc.contributor.advisor | Riviere, Beatrice M. | |
| dc.contributor.committeeMember | Heinkenschloss, Matthias | |
| dc.contributor.committeeMember | Symes, William W. | |
| dc.creator | Tan, Jun | |
| dc.date.accessioned | 2014-10-14T15:19:03Z | |
| dc.date.available | 2014-10-14T15:19:03Z | |
| dc.date.created | 2013-12 | |
| dc.date.issued | 2013-09-23 | |
| dc.date.submitted | December 2013 | |
| dc.date.updated | 2014-10-14T15:19:03Z | |
| dc.description.abstract | This thesis analyzes a numerical method for solving the poroelasticity equations. The model incorporating the poroelasticity equations in this thesis can be applied in intestinal edema, which is a medical condition referring to the accumulation of excess fluid in the spaces between cells of intestinal wall tissue. The model has a dilatation term and can give a comprehensive prediction of pressure and displacement for intestinal edema. I approximate the pressure, displacement and dilatation by the discontinuous Galerkin method, which includes symmetric, nonsymmetric and incomplete interior penalty Galerkin cases. Moreover, in order to solve for the nonsymmetric case, I introduce an additional penalty term in the scheme. Theoretical convergence error estimates derived in a discrete-in-time setting show the a priori error can be bounded by some constant, which is related to the pressure, displacement, dilatation and the mesh size. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Tan, Jun. "Convergence Analysis of Discontinuous Galerkin Methods for Poroelasticity Equations." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77564">https://hdl.handle.net/1911/77564</a>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/77564 | |
| dc.language.iso | eng | |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | |
| dc.subject | Discontinuous Galerkin methods | |
| dc.subject | Poroelasticity equations | |
| dc.subject | Error estimate | |
| dc.subject | Intestinal edema | |
| dc.subject | Numerical PDE | |
| dc.title | Convergence Analysis of Discontinuous Galerkin Methods for Poroelasticity Equations | |
| dc.type | Thesis | |
| dc.type.material | Text | |
| thesis.degree.department | Computational and Applied Mathematics | |
| thesis.degree.discipline | Engineering | |
| thesis.degree.grantor | Rice University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Arts |