Abstract
Explicit generators for high-order (r>1) scalar and vector finite element spaces generally used in numerical electromagnetism are presented and classical degrees of freedom, the so-called moments, revisited. Properties of these generators on simplicial meshes are investigated, and a general technique to restore duality between moments and generators is proposed. Algebraic and exponential optimal h- and r-error rates are numerically validated for high-order edge elements on the problem of Maxwell’s eigenvalues in a square domain.
| Original language | English |
|---|---|
| Pages (from-to) | 111-136 |
| Number of pages | 26 |
| Journal | Numerical Algorithms |
| Volume | 74 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2017 |
| Externally published | Yes |
Keywords
- Degrees of freedom and generators in duality
- High-order FEs in electromagnetism
- Simplices