奇异半线性抛物方程的时空有限元方法

The Space-Time Finite Element Method for Semi-linear Parabolic Problem with Singularity

探讨研究了一类半线性抛物方程的自适应有限元方法,即时间间断、空间连续的间断时空有限元方法.把有限元方法和有限差分方法相结合,不对时空网格施加限制条件,证明了弱解的存在唯一性,给出了有限元解的时间最大模、空间加权L2模,即L∞(L2b)模误差估计.

An adaptive space-time finite element method,continuous in space but discontinuous in time,for a class of semi-linear singular parabolic problem is investigated based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on the choice of space-time meshes. The error estimate in L^∞ （Lb^2） norm,that is maximum norm in time,and the weighted L^2 norm in space are obtained.