A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.
","abstract_html":"<p>A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.</p>","abstract_has_math":false,"creators":["Brown, Robert Gregory"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Richard Noren","Hideaki Kaneko","Jin Wang","Dimitrie C. Popescu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-07-01T07:00:00Z","date_published":"2010-07-01T07:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Discontinuous Galerkin method","Multiresolution wavelet","Applied Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["A Solution of the Heat Equation with the Discontinuous Galerkin Method Using a Multilivel Calculation Method That Utilizes a Multiresolution Wavelet Basis"]}]}],"canonical_facts":{"dc:contributor":["Richard Noren","Hideaki Kaneko","Jin Wang","Dimitrie C. Popescu"],"dc:creator":["Brown, Robert Gregory"],"dc:date.available":["2019-06-05T07:00:00Z"],"dc:description.abstract":["A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.
"],"dc:identifier":["9781124291796","https://digitalcommons.odu.edu/mathstat_etds/7"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Discontinuous Galerkin method","Multiresolution wavelet","Applied Mathematics"],"dc:title":["A Solution of the Heat Equation with the Discontinuous Galerkin Method Using a Multilivel Calculation Method That Utilizes a Multiresolution Wavelet Basis"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}