@Article{IJNAM-1-2,
author = {Pani, K., A. and Sinha, R., K. and Otta, K., A.},
title = {An $H^1$-Galerkin Mixed Method for Second Order Hyperbolic Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2004},
volume = {1},
number = {2},
pages = {111--130},
abstract = {<p style="text-align: justify;">An $H^1$-Galerkin mixed finite element method is discussed for
a class of second order hyperbolic problems. It is proved that the Galerkin
approximations have the same rates of convergence as in the classical mixed
method, but without LBB stability condition and quasi-uniformity requirement
on the finite element mesh. Compared to the results proved for one space
variable, the $L^∞(L^2)$-estimate of the stress is not optimal with respect to the
approximation property for the problems in two and three space dimensions.
It is further noted that if the Raviart- Thomas spaces are used for approximating
the stress, then optimal estimate in $L^∞(L^2)$-norm is achieved using the
new formulation. Finally, without restricting the approximating spaces for the
stress, a modification of the method is proposed and analyzed. This confirms
the findings in a single space variable and also improves upon the order of convergence
of the classical mixed procedure under an extra regularity assumption
on the exact solution.</p>},
issn = {2617-8710},
doi = {https://doi.org/2004-IJNAM-969},
url = {https://global-sci.com/article/83896/an-h1-galerkin-mixed-method-for-second-order-hyperbolic-equations}
}