二维拟线性奇异抛物问题的时空间断有限元法

The Discontinuous Space-Time Finite Element Method for Two-dimensional Quasilinear Parabolic Equation with Singularities

将时间允许间断而空间连续的时空有限元方法应用于二维拟线性奇异问题,利用线性化的方法,化为线性抛物方程予以处理,证明加权索伯列夫空间模意义下的有限元解的误差估计,包括在允许的时间间断点tn处,有限元解产生跳跃时的误差,最后再给出原方程的误差估计.

A space-time finite element method ,continuous in space but discontinuous in time ,for two-dimensional quasilinear problems with singularities is discussed. The primary equation is linearized to a linear parabolic problems by linearized technique. The error estimates in weighted sobolev norm are derived for linearized problems, including the jump error at the permitted discontinuous time level tn. Finally,the error estimates for the primary equation is obtained.