- 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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