On the convergence of a low order Lagrange finite element approach for natural convection problems
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and temperature) is well-posed if used with a penalty term in the dive...
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| creator | Danaila, Ionut Luddens, Francky Legrand, Cécile |
| description | The purpose of this article is to study the convergence of a low order finite
element approximation for a natural convection problem. We prove that the
discretization based on P1 polynomials for every variable (velocity, pressure
and temperature) is well-posed if used with a penalty term in the divergence
equation, to compensate the loss of an inf-sup condition. With mild assumptions
on the pressure regularity, we recover convergence for the
Navier-Stokes-Boussinesq system, provided the penalty term is chosen in
accordance with the mesh size. We express conditions to obtain optimal order of
convergence. We illustrate theoretical convergence results with extensive
examples. The computational cost that can be saved by this approach is also
assessed. |
| doi_str_mv | 10.48550/arxiv.2207.12732 |
| format | Article |
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element approximation for a natural convection problem. We prove that the
discretization based on P1 polynomials for every variable (velocity, pressure
and temperature) is well-posed if used with a penalty term in the divergence
equation, to compensate the loss of an inf-sup condition. With mild assumptions
on the pressure regularity, we recover convergence for the
Navier-Stokes-Boussinesq system, provided the penalty term is chosen in
accordance with the mesh size. We express conditions to obtain optimal order of
convergence. We illustrate theoretical convergence results with extensive
examples. The computational cost that can be saved by this approach is also
assessed.</description><identifier>DOI: 10.48550/arxiv.2207.12732</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2022-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2207.12732$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2207.12732$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Danaila, Ionut</creatorcontrib><creatorcontrib>Luddens, Francky</creatorcontrib><creatorcontrib>Legrand, Cécile</creatorcontrib><title>On the convergence of a low order Lagrange finite element approach for natural convection problems</title><description>The purpose of this article is to study the convergence of a low order finite
element approximation for a natural convection problem. We prove that the
discretization based on P1 polynomials for every variable (velocity, pressure
and temperature) is well-posed if used with a penalty term in the divergence
equation, to compensate the loss of an inf-sup condition. With mild assumptions
on the pressure regularity, we recover convergence for the
Navier-Stokes-Boussinesq system, provided the penalty term is chosen in
accordance with the mesh size. We express conditions to obtain optimal order of
convergence. We illustrate theoretical convergence results with extensive
examples. The computational cost that can be saved by this approach is also
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element approximation for a natural convection problem. We prove that the
discretization based on P1 polynomials for every variable (velocity, pressure
and temperature) is well-posed if used with a penalty term in the divergence
equation, to compensate the loss of an inf-sup condition. With mild assumptions
on the pressure regularity, we recover convergence for the
Navier-Stokes-Boussinesq system, provided the penalty term is chosen in
accordance with the mesh size. We express conditions to obtain optimal order of
convergence. We illustrate theoretical convergence results with extensive
examples. The computational cost that can be saved by this approach is also
assessed.</abstract><doi>10.48550/arxiv.2207.12732</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | On the convergence of a low order Lagrange finite element approach for natural convection problems |
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