【摘要】 针对热耦合的斯托克斯流方程组的解析解给出了其存在性以及正则性的分析.给出此方程组多解情形下的有限元格式,并且证明了此非线性问题数值解的存在性.研究方程的非奇异解的逼近性质的同时,证明了有限元解的收敛性.在Lp理论下给出了其最优的误差估计.更多还原

【Abstract】 A stationary Stokes flow with thermal effect is studied both mathematically in general cases and numerically.The existence and regularity of weak solutions are established by a special method.Nonlinear finite element approximations are proposed and analyzed.The existence and convergence of the nonlinear finite element schemes are proved.Optimal error estimates in Lp-norm to the nonsingular solutions are obtained.更多还原