TY - JOUR
T1 - AD Galerkin Analysis for Nonlinear Pseudo-Hyperbolic Equations
AU -  Xia Cui 
JO - Journal of Computational Mathematics
VL - 2
SP - 125
EP - 134
PY - 2003
DA - 2003/04
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8875.html
KW - nonlinear, pseudo-hyperbolic equation, alternating direction, numerical analysis.
AB - <p style="text-align: justify;">AD (Alternating direction) Galerkin schemes for $d$-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal $H^1$ and $L^2$ convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.</p>