ROBUST DPG TEST SPACES AND FORTIN OPERATORS---THE H<SUP>1</SUP> AND H(div) CASES

Simple item page
dc.contributor.authorFuhrer, Thomas
dc.contributor.authorHeuer, Norbert
dc.date.accessioned2025-01-20T17:07:27Z
dc.date.available2025-01-20T17:07:27Z
dc.date.issued2024
dc.description.abstractAt the fully discrete setting, stability of the discontinuous Petrov-Galerkin (DPG) method with optimal test functions requires local test spaces that ensure the existence of Fortin operators. We construct such operators for H1 and H(div) on simplices in any space dimension and arbitrary polynomial degree. The resulting test spaces are smaller than previously analyzed cases. For parameter-dependent norms, we achieve uniform boundedness by the inclusion of face bubble functions that are polynomials on faces and decay exponentially in the interior. As an example, we consider a canonical DPG setting for reaction-dominated diffusion. Our test spaces guarantee uniform stability and quasi-optimal convergence of the scheme. We present numerical experiments that illustrate the loss of stability and error control by the residual for small diffusion coefficient when using standard polynomial test spaces, whereas we observe uniform stability and error control with our construction.
dc.description.funderANID through FONDECYT
dc.fuente.origenWOS
dc.identifier.doi10.1137/23M1550360
dc.identifier.eissn1095-7170
dc.identifier.issn0036-1429
dc.identifier.urihttps://doi.org/10.1137/23M1550360
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90857
dc.identifier.wosidWOS:001178520700004
dc.issue.numero2
dc.language.isoen
dc.pagina.final748
dc.pagina.inicio718
dc.revistaSiam journal on numerical analysis
dc.rightsacceso restringido
dc.subjectDPG method
dc.subjectFortin operators
dc.subjectsingularly perturbed problems
dc.subjectreaction-diffusion
dc.titleROBUST DPG TEST SPACES AND FORTIN OPERATORS---THE H<SUP>1</SUP> AND H(div) CASES
dc.typeartículo
dc.volumen62
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Collections
Artículos de revistas