【摘要】 针对变系数椭圆型方程矩形元,证明了能量积分的渐近展开具有如下的乘积定理:∫Ω∫Ωk2jh2iFi(D2i-2Gj(D2j-2B(w,uh)=∑ny(uyyφ))vhdxdy+ex(uxxφ))vhdxdy+∑nei=1j=1∫Ω∑nh2i[Fij(D2i-2eek2jxD2j-2y(uyyφ))]vhdxdy+Rn,h.xD2jy(uxxφ))+Gij(D2ii+j=2更多还原

【Abstract】 For the elliptic partial differential equations of variable coefficient,we obtain the product theorem of asymptotic expansions of energy integral as follows:B（w,v_h）=∑ni=1h²ⁱ_e∫_ΩF_i(D^2i-2_x(v_xxφ))v_hdxdy+∑nj=1k^2j_e∫_ΩG_j(D^2j-2_y(u_yyφ))u_hdxdy+∑ni+j=2h²ⁱ_ek^2j_e∫_Ω[F_ij(D^2i-2_xD^2j_y(u_xxφ))+G_ij(D²ⁱ_xD^2j-2_y(u_yyφ))]v_hdxdy+R_n,h.更多还原