A projection scheme for the numerical solution of the incompressible Navier-Strokes equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. The main advantage of the method is that is does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit scheme is used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient.
","abstract_html":"<p>A projection scheme for the numerical solution of the incompressible Navier-Strokes equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. The main advantage of the method is that is does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit scheme is used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient.</p>","abstract_has_math":false,"creators":["Kyriazis, Nikolaos"],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-11-01T07:00:00Z","date_published":"2014-11-01T07:00:00Z","updated_at":"2026-07-27T19:26:08Z","subjects":["finite element method","3D","incompressible","flow","Aerospace Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/273","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kyriazis, Nikolaos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["finite element method","3D","incompressible","flow","Aerospace Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/273"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A projection scheme for the numerical solution of the incompressible Navier-Strokes equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. The main advantage of the method is that is does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit scheme is used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient.
"]},{"key":"dc:title","label":"Title","values":["A Continuous/Discontinuous FE Method for the 3D Incompressible Flow Equations"]}]}],"canonical_facts":{"dc:creator":["Kyriazis, Nikolaos"],"dc:description.abstract":["A projection scheme for the numerical solution of the incompressible Navier-Strokes equation is presented. Finite element discontinuous Galerkin (dG) discretization for the velocity in the momentum equations is employed. The incompressibility constraint is enforced by numerically solving the Poisson equation for pressure using a continuous Galerkin (cG) discretization. The main advantage of the method is that is does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition, thus equal order finite element approximations for both velocity and pressure can be used. Furthermore, by using cG discretization for the Poisson equation, no auxiliary equations are needed as it is required for dG approximations of second order derivatives. In order to enable large time steps for time marching to steady-state and time evolving problems, implicit scheme is used in connection with high order implicit RK methods. Numerical tests demonstrate that the overall scheme is accurate and computationally efficient.
"],"dc:identifier":["https://commons.erau.edu/edt/273"],"dc:subject":["finite element method","3D","incompressible","flow","Aerospace Engineering"],"dc:title":["A Continuous/Discontinuous FE Method for the 3D Incompressible Flow Equations"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:26:08Z"}