Variational and Geometric
Aspects
of Compatible Discretizations
How different people discretize
A sequence of linear
systems vs.
a single linear system
A summary of variational settings for FEM
What does variational compatibility buy you
What does variational
compatibility
say about the other issues?
Problems with identical reduced systems
How to achieve geometric compatibility?
Algebraic Topology Approach
1. System reduction
Algebraic Topology Approach
2. Inner products and dual operators
Algebraic Topology Framework: Summary
Direct discretization of a div-curl system
Direct discretization of a div-grad system
What does geometric compatibility buy you?
There’s only one low-order
compatible method