A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements. Issue 3 (21st December 2020)

• Record Type: Journal Article
• Authors: Banz, Lothar; Ilyas, Muhammad; Lamichhane, Bishnu P.; McLean, William; Stephan, Ernst P.
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 3(2021)
• Page Start: 2429
• Page End: 2445
• Publication Date: 2020-12-21
• Subjects: a priori error estimate -- biorthogonal -- mixed finite element method -- Poisson problem -- saddle‐point problem; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22722
• Languages: English
• ISSNs: 0749-159X

Abstract

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.