Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2429-2445 |
| Seitenumfang | 17 |
| Fachzeitschrift | Numerical Methods for Partial Differential Equations |
| Jahrgang | 37 |
| Ausgabenummer | 3 |
| Frühes Online-Datum | 21 Dez. 2020 |
| Publikationsstatus | Veröffentlicht - 29 März 2021 |
Abstract
We use a three-field mixed formulation of the Poisson equation to develop a mixed finite element method using Raviart–Thomas elements. We use a locally constructed biorthogonal system for Raviart–Thomas finite elements to improve the computational efficiency of the approach. We analyze the existence, uniqueness and stability of the discrete problem and show an a priori error estimate. We also develop an a posteriori error estimate for our formulation. Numerical results are presented to demonstrate the performance of our approach.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Numerical Methods for Partial Differential Equations, Jahrgang 37, Nr. 3, 29.03.2021, S. 2429-2445.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements
AU - Banz, Lothar
AU - Ilyas, Muhammad
AU - Lamichhane, Bishnu P.
AU - McLean, William
AU - Stephan, Ernst P.
PY - 2021/3/29
Y1 - 2021/3/29
N2 - We use a three-field mixed formulation of the Poisson equation to develop a mixed finite element method using Raviart–Thomas elements. We use a locally constructed biorthogonal system for Raviart–Thomas finite elements to improve the computational efficiency of the approach. We analyze the existence, uniqueness and stability of the discrete problem and show an a priori error estimate. We also develop an a posteriori error estimate for our formulation. Numerical results are presented to demonstrate the performance of our approach.
AB - We use a three-field mixed formulation of the Poisson equation to develop a mixed finite element method using Raviart–Thomas elements. We use a locally constructed biorthogonal system for Raviart–Thomas finite elements to improve the computational efficiency of the approach. We analyze the existence, uniqueness and stability of the discrete problem and show an a priori error estimate. We also develop an a posteriori error estimate for our formulation. Numerical results are presented to demonstrate the performance of our approach.
KW - a priori error estimate
KW - biorthogonal
KW - mixed finite element method
KW - Poisson problem
KW - saddle-point problem
UR - http://www.scopus.com/inward/record.url?scp=85097833386&partnerID=8YFLogxK
U2 - 10.1002/num.22722
DO - 10.1002/num.22722
M3 - Article
AN - SCOPUS:85097833386
VL - 37
SP - 2429
EP - 2445
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
SN - 0749-159X
IS - 3
ER -