Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements
Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements
复制标题
三角形单元任意阶非相容有限元逼近误差的完全可计算界
DOI：
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发表时间：
2008
影响因子：
2.9
通讯作者：
Richard Rankin
中科院分区：
文献类型：
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作者：
M. Ainsworth;Richard Rankin
我们得到了一个完全可计算的后验误差界的断裂能量模的误差在任意阶三角形的线性二阶椭圆问题的变渗透率的有限元逼近。该估计是完全免费的未知常数，并提供了一个有保证的数值界上的错误的能量范数。该估计被证明是有效的，在这个意义上，它也提供了一个下界的破碎的能量范数的错误高达一个常数和高阶数据振荡项。
We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms.