非矩形区域上非线性抛物型方程组的方向交替GALERKIN方法

GALERKIN ALTERNATING-DIRECTION METHODS FOR NONLINEAR PARABOLIC SYSTEMS ON NONRECTANGULAR REGIONS

利用等参变换、在局部有限单元上近似Ｊａｃｏｂｉ行列式ｐ（ｘ）及系数ｑｉ（ξ，ｕ），１≤ｉ≤ｋ等方法，对非矩形区域上非线性抛物型方程组ｑｉ（ξ，ｕ）ｕｉｔ－∑ｋｊ＝１·（ａ～ｉｊ（ξ，ｕ）ｕｊ）＋∑ｋｊ＝１ｂ～→ｉｊ（ξ，ｕ）·ｕｊ＝ｆｉ（ξ，ｔ，ｕ），１≤ｉ≤ｋ，提出了一类方向交替Ｇａｌｅｒｋｉｎ格式，并得到最优的Ｌ２－和Ｈ１－误差估计．

Galerkin alternating-direction procedures are considered for the nonlinear parabolic systems q i(ξ,u)u it-∑kj=1·(a～ ij (ξ,u)u j)+∑kj=1 b～ → ij (ξ,u)·u j=f i(ξ,t,u),1≤i≤k. Isoparametric elements and an approximation to the Jacobian of the isoparametric map which is based on patches of finite elements are used.Optimal order L 2-and H 1-error estimates are derived.