抛物方程的时空有限元方法

基金项目: 国家自然科学基金资助项目(19771083);美国国家科学基金资助项目(No.INT9601084)

The Space-Time Finite Element Method for Parabolic Problems

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P R China

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。
- 半线性抛物方程 /
- 时空有限元方法 /
- 存在唯一 /
- 误差估计
Abstract: 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.
- semi-linear parabolic equations /
- space time finite element method /
- existence and uniquess /
- error estimate

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