TY - JOUR
T1 - A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems
AU - Lamichhane, Bishnu P.
PY - 2011/3
Y1 - 2011/3
N2 - We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optimal a priori estimates for both stream function and vorticity, and present numerical results to demonstrate the efficiency of the approach.
AB - We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optimal a priori estimates for both stream function and vorticity, and present numerical results to demonstrate the efficiency of the approach.
KW - Biharmonic problem
KW - Biorthogonal or quasi-biorthogonal system
KW - Mixed finite elements
UR - http://www.scopus.com/inward/record.url?scp=79751530465&partnerID=8YFLogxK
U2 - 10.1007/s10915-010-9409-7
DO - 10.1007/s10915-010-9409-7
M3 - Article
SN - 0885-7474
VL - 46
SP - 379
EP - 396
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 3
ER -