In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.
","abstract_html":"<p>In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.</p>","abstract_has_math":false,"creators":["Cornthwaite, John"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Scott Kersey","Yan Wu","Cheng Zhang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-01-01T08:00:00Z","date_published":"2013-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:41Z","subjects":["ETD","Navier-Stokes","Pressure Poisson Equation","Galerkin Finite Element","Applied Mathematics","Mathematics","Numerical Analysis and Computation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/831","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Scott Kersey","Yan Wu","Cheng Zhang"]},{"key":"dc:creator","label":"Author","values":["Cornthwaite, John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-09-17T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Navier-Stokes","Pressure Poisson Equation","Galerkin Finite Element","Applied Mathematics","Mathematics","Numerical Analysis and Computation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/831"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.
"]},{"key":"dc:title","label":"Title","values":["Pressure Poisson Method for the Incompressible Navier-Stokes Equations Using Galerkin Finite Elements"]}]}],"canonical_facts":{"dc:contributor":["Scott Kersey","Yan Wu","Cheng Zhang"],"dc:creator":["Cornthwaite, John"],"dc:date.available":["2013-09-17T07:00:00Z"],"dc:description.abstract":["In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/831"],"dc:subject":["ETD","Navier-Stokes","Pressure Poisson Equation","Galerkin Finite Element","Applied Mathematics","Mathematics","Numerical Analysis and Computation"],"dc:title":["Pressure Poisson Method for the Incompressible Navier-Stokes Equations Using Galerkin Finite Elements"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:41Z"}