Details
| Original language | English |
|---|---|
| Pages (from-to) | 2429-2445 |
| Number of pages | 17 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 37 |
| Issue number | 3 |
| Early online date | 21 Dec 2020 |
| Publication status | Published - 29 Mar 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.
Keywords
- a priori error estimate, biorthogonal, mixed finite element method, Poisson problem, saddle-point problem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Numerical Methods for Partial Differential Equations, Vol. 37, No. 3, 29.03.2021, p. 2429-2445.
Research output: Contribution to journal › Article › Research › 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 -