Finite element solution of diffusion problems with irregular data
Finite element solution of diffusion problems with irregular data
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DOI：
10.1007/bf01390130
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发表时间：
1984-06
影响因子：
2.1
通讯作者：
R. Rannacher
中科院分区：
文献类型：
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作者：
R. Rannacher
在实际应用中，扩散问题的初始或边界数据常常不规则，导致解的正则性局部失效。除非采取某些预防措施，否则这可能会大大降低整个积分区间内离散化方案的精度。2μ阶对角Padé格式与标准的有限元离散相结合，通常需要一个不自然的步长限制，以达到甚至局部最优的精度。这里示出，这种限制可以通过保持离散化的阶数并且在μ=1的情况下不增加成本的样本阻尼过程来避免。
Diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break-down of the solution's regularity. This may drastically reduce the accuracy of discretization schemes over the whole interval of integration, unless certain precautions are taken. The diagonal Padé schemes of order 2μ, combined with a standard finite element discretization, usually require an unnatural step size restriction in order to achieve even locally optimal accuracy. It is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and, in the case μ=1, does not increase the costs.