A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart-Thomas elements

Title: A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart-Thomas elements
Creator: Banz, Lothar; Ilyas, Muhammad; Lamichhane, Bishnu P.; McLean, William; Stephan, Ernet P.
Relation: Numerical Methods for Partial Differential Equations Vol. 37, Issue 3, p. 2429-2445
Publisher Link: http://dx.doi.org/10.1002/num.22722
Publisher: John Wiley & Sons
Resource Type: journal article
Date: 2021
Description: 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.
Subject: a priori error estimate; biorthogonal; mixed finite element method; Poisson problem; saddle-point problem
Identifier: http://hdl.handle.net/1959.13/1470105
Identifier: uon:48381
Identifier: ISSN:0749-159X
Language: eng
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