摘要
讨论了一类半线性抛物方程的自适应有限元方法 ,即空间连续、时间间断的时空有限元方法· 利用有限元方法和有限差分方法相结合的技巧 ,不对时空网格施加限制条件 ,证明弱解的存在唯一 ,并且给出了时间最大模、空间L2 模 ,即L∞(L2 )模的误差估计 ,同时给出了数值分析结果 ,并对理论结果作了验证·
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is 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 choice of the space-time meshes. Basic error estimates in L∞(L2) norm, that is maximum-norm in time, L2 -norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
出处
《应用数学和力学》
EI
CSCD
北大核心
2001年第6期613-624,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金!资助项目 ( 197710 83)
美国国家科学基金!资助项目 (No .INT 960 10 84 )
