Approximation properties of primal discontinuous Petrov-Galerkin method on general quadrilateral meshes
Niemi, Antti H. (2023-10-13)
Elsevier
13.10.2023
Niemi, A. H. (2023). Approximation properties of primal discontinuous Petrov-Galerkin method on general quadrilateral meshes. In Computers & Mathematics with Applications (Vol. 151, pp. 300–303). Elsevier BV. https://doi.org/10.1016/j.camwa.2023.09.015.
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© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
https://creativecommons.org/licenses/by/4.0/
© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202312073547
https://urn.fi/URN:NBN:fi:oulu-202312073547
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Abstract
We consider the approximation properties of primal discontinuous Petrov-Galerkin (DPG) method on quadrilateral meshes. We show how the previous convergence results as well as the Aubin-Nitsche type duality arguments can be extended to cover arbitrary convex quadrilateral elements with bilinear isomorphisms. The arguments are based on the approximation theory of quadrilateral vector finite element spaces associated to the numerical flux variable of the DPG approximation. The theoretical results are validated by a numerical experiment that features also a comparison between the primal DPG method and a conventional least squares finite element method with the same number of degrees of freedom.
We consider the approximation properties of primal discontinuous Petrov-Galerkin (DPG) method on quadrilateral meshes. We show how the previous convergence results as well as the Aubin-Nitsche type duality arguments can be extended to cover arbitrary convex quadrilateral elements with bilinear isomorphisms. The arguments are based on the approximation theory of quadrilateral vector finite element spaces associated to the numerical flux variable of the DPG approximation. The theoretical results are validated by a numerical experiment that features also a comparison between the primal DPG method and a conventional least squares finite element method with the same number of degrees of freedom.
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