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A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations. / Korneev, V.

In: Lobachevskii Journal of Mathematics, Vol. 45, No. 6, 01.06.2024, p. 2843-2852.

Research output: Contribution to journal › Article › peer-review

Harvard

Korneev, V 2024, 'A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations', Lobachevskii Journal of Mathematics, vol. 45, no. 6, pp. 2843-2852. https://doi.org/10.1134/s1995080224602947

APA

Korneev, V. (2024). A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations. Lobachevskii Journal of Mathematics, 45(6), 2843-2852. https://doi.org/10.1134/s1995080224602947

Vancouver

Korneev V. A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations. Lobachevskii Journal of Mathematics. 2024 Jun 1;45(6):2843-2852. https://doi.org/10.1134/s1995080224602947

Author

Korneev, V. / A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations. In: Lobachevskii Journal of Mathematics. 2024 ; Vol. 45, No. 6. pp. 2843-2852.

BibTeX

@article{b0f421c777bb4f0faee4ab89e901398f,
title = "A Posteriori Error Bounds for Mixed FEM{\textquoteright}s with Curvilinear Finite Elements for -Order Elliptic Equations",
abstract = "Abstract: A reliable and computable a posteriori error bound is derived for the mixed Ciarlet–Raviart method for the equation,, with the first boundary condition and a piecewise constant. Several authors derived residual type a posteriori error bounds at assumptions that and the domain is polygonal, none of which is used in the paper. In case of a piecewise smooth boundary, we consider the mixed method with the triangular Lagrange finite elements of the order, which, in general, are curvilinear along the boundary. This provides an approximation to the boundary, matching the finite elements in accuracy. Our bounds belong to the class of a posteriori functional majorants and are evaluated with help of functions from the testing space. By the reasons of accuracy and simplicity, this space is generated by the finite elements with the domains, coinciding with the domains of the Lagrange elements, and singular rational coordinate functions. {\textcopyright} Pleiades Publishing, Ltd. 2024.",
keywords = "curvilinear finite elements, order elliptic equations, a posteriori error bounds, higher order methods, mixed finite element method, singularly perturbed elliptic equations",
author = "V. Korneev",
note = "Export Date: 21 October 2024 Адрес для корреспонденции: Korneev, V.; St. Petersburg State UniversityRussian Federation; эл. почта: vad.korneev2011@yandex.ru",
year = "2024",
month = jun,
day = "1",
doi = "10.1134/s1995080224602947",
language = "Английский",
volume = "45",
pages = "2843--2852",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Pleiades Publishing",
number = "6",

}

RIS

TY - JOUR

T1 - A Posteriori Error Bounds for Mixed FEM’s with Curvilinear Finite Elements for -Order Elliptic Equations

AU - Korneev, V.

N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Korneev, V.; St. Petersburg State UniversityRussian Federation; эл. почта: vad.korneev2011@yandex.ru

PY - 2024/6/1

Y1 - 2024/6/1

N2 - Abstract: A reliable and computable a posteriori error bound is derived for the mixed Ciarlet–Raviart method for the equation,, with the first boundary condition and a piecewise constant. Several authors derived residual type a posteriori error bounds at assumptions that and the domain is polygonal, none of which is used in the paper. In case of a piecewise smooth boundary, we consider the mixed method with the triangular Lagrange finite elements of the order, which, in general, are curvilinear along the boundary. This provides an approximation to the boundary, matching the finite elements in accuracy. Our bounds belong to the class of a posteriori functional majorants and are evaluated with help of functions from the testing space. By the reasons of accuracy and simplicity, this space is generated by the finite elements with the domains, coinciding with the domains of the Lagrange elements, and singular rational coordinate functions. © Pleiades Publishing, Ltd. 2024.

AB - Abstract: A reliable and computable a posteriori error bound is derived for the mixed Ciarlet–Raviart method for the equation,, with the first boundary condition and a piecewise constant. Several authors derived residual type a posteriori error bounds at assumptions that and the domain is polygonal, none of which is used in the paper. In case of a piecewise smooth boundary, we consider the mixed method with the triangular Lagrange finite elements of the order, which, in general, are curvilinear along the boundary. This provides an approximation to the boundary, matching the finite elements in accuracy. Our bounds belong to the class of a posteriori functional majorants and are evaluated with help of functions from the testing space. By the reasons of accuracy and simplicity, this space is generated by the finite elements with the domains, coinciding with the domains of the Lagrange elements, and singular rational coordinate functions. © Pleiades Publishing, Ltd. 2024.

KW - curvilinear finite elements

KW - order elliptic equations

KW - a posteriori error bounds

KW - higher order methods

KW - mixed finite element method

KW - singularly perturbed elliptic equations

UR - https://www.mendeley.com/catalogue/9e5111ee-028a-3672-a1be-d0c82d4a182c/

U2 - 10.1134/s1995080224602947

DO - 10.1134/s1995080224602947

M3 - статья

VL - 45

SP - 2843

EP - 2852

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 6

ER -

ID: 126220272