Abstract
A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order | convergence rates in the L 2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number of nonzero entries in the stiffness matrix is also proposed and analyzed. Finally, numerical results are presented to illustrate the theoretical analysis.
| Original language | English |
|---|---|
| Pages (from-to) | 55-76 |
| Number of pages | 22 |
| Journal | Mathematical Modelling and Numerical Analysis |
| Volume | 41 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2007 |
Keywords
- Finite elements
- First-order PDE's
- Friedrichs' systems
- Interior penalty
- Stabilization methods