Recently there has been a lot of interest in the systematic study of discrete function spaces and their properties. In this seminar we will discuss the classification of various finite element spaces in the language of discrete exterior calculus. We will see that many well known finite element families arise as special cases. We will work with the Acta Numerica article by Arnold, Falk, and Winther (2006). See also this summary page on finite element classification.
Basic knowledge standard and mixed finite element methods for elliptic PDEs and saddle point systems will be advantageous.
The seminar takes place on Mondays at 3:00pm c.t. in room 5.002, Wegelerstr. 6.
|18.05.15||CA||Exterior algebra and exterior calculus|
|01.06.15||CS||Polynomial differential forms and the Koszul complex|
|08.06.15||JK||Polynomial differential forms on a simplex|
|22.06.15||NR||Finite element differential forms and their cohomology|
|29.06.15||SB||The Hodge Laplacian|