an:01764396
Zbl 1032.74049
B??cache, E.; Joly, P.; Tsogka, C.
A new family of mixed finite elements for the linear elastodynamic problem
EN
SIAM J. Numer. Anal. 39, No. 6, 2109-2132 (2002).
00086225
2002
j
74S05 74H15 65M12 65M60 65M15
velocity-stress formulation; convergence; error estimates; elliptic problem; regularity; mass lumping; evolution problem
The authors develop and analyze a new family of mixed finite elements for velocity-stress formulation of elastodynamics. For both stationary and evolution problems, the convergence of solution in \(L^2\) norm is obtained. These results are valid for any finite element space of order \(k\), and a generalization of these results to three-dimensional case is straightforward. The error estimates obtained for an elliptic problem give the same convergence rate, assuming less regularity of the solution. Convergence is obtained with regularity \(H^1(\Omega)\) for the velocity. For the solution of evolution problem, error estimates are given in \(C(0,T;H(\text{div}))\), but they require more regularity with respect to time. Related results can be found in [\textit{E. B\(\acute{e}\)cache, P. Joly and C. Tsogka}, C. R. Acad. Sci., Paris, S??r. I, Math. 325, 545-550 (1997; Zbl 0895.73064); SIAM. J. Numer. Anal. 37, 1053-1084 (2000; Zbl 0958.65102) and \textit{J. C. N??d??lec}, Numer. Math. 50, 57-81 (1986; Zbl 0625.65107)].
Nicolae Pop (Baia Mare)
Zbl 0895.73064; Zbl 0958.65102; Zbl 0625.65107