TY - GEN
T1 - A generalization for stable mixed finite elements
AU - Gillette, Andrew
AU - Bajaj, Chandrajit
PY - 2010
Y1 - 2010
N2 - Mixed finite element methods solve a PDE involving two or more variables. In typical problems from electromagnetics and electrodiffusion, the degrees of freedom associated to the different variables are stored on both primal and dual domain meshes and a discrete Hodge star is used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the model and numerical stability of a finite element method. We also show how to define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods.
AB - Mixed finite element methods solve a PDE involving two or more variables. In typical problems from electromagnetics and electrodiffusion, the degrees of freedom associated to the different variables are stored on both primal and dual domain meshes and a discrete Hodge star is used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the model and numerical stability of a finite element method. We also show how to define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods.
UR - http://www.scopus.com/inward/record.url?scp=77958066464&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77958066464&partnerID=8YFLogxK
U2 - 10.1145/1839778.1839785
DO - 10.1145/1839778.1839785
M3 - Conference contribution
AN - SCOPUS:77958066464
SN - 9781605589848
T3 - Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
SP - 41
EP - 50
BT - Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
T2 - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
Y2 - 1 September 2010 through 3 September 2010
ER -