A second-order finite element method with mass lumping for Maxwell’s equations on tetrahedra. (English) Zbl 1464.35341
Summary: We consider the numerical approximation of Maxwell’s equations in the time domain by a second-order \(H(\mathrm{curl})\) conforming finite element approximation. In order to enable the efficient application of explicit time-stepping schemes, we utilize a mass-lumping strategy resulting from numerical integration in conjunction with the finite element spaces introduced in [A. Elmkies and P. Joly, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 11, 1217–1222 (1997; Zbl 0893.65068)]. We prove that this method is second-order accurate if the true solution is divergence free but the order of accuracy reduces to one in the general case. We then propose a modification of the finite element space, which yields second-order accuracy in the general case.
MSC:
| 35Q61 | Maxwell equations |
| 78A25 | Electromagnetic theory (general) |
| 78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Citations:
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