A METHOD WITH PENALIZED RIGHT HAND SIDE FOR THE NUMERICAL RESOLUTION OF THE CURL CURL EQUATION

Marion Darbas (1) , Jérémy Heleine (1) , S Lohrengel (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LMR - Laboratoire de Mathématiques de Reims

A new method is proposed to solve numerically the curl curl equation by means of edge finite elements. In a first step, a compatible right hand side that belongs exactly to the range of the singular curl curl matrix is computed by penalization. In a second step, a Conjugate Gradient solver computes a discretely gauged solution of the curl curl equation. Convergence results are proven both in terms of the penalization parameter and the mesh size. Numerical simulations in two dimensions corroborate the theoretical results.

Domaines: Analyse numérique [math.NA]

Marion Darbas, Jérémy Heleine, S Lohrengel. A METHOD WITH PENALIZED RIGHT HAND SIDE FOR THE NUMERICAL RESOLUTION OF THE CURL CURL EQUATION. 2018. ⟨hal-01681590⟩