A-POSTERIORI ERROR ESTIMATES FOR FINITE-ELEMENT METHOD
A-POSTERIORI ERROR ESTIMATES FOR FINITE-ELEMENT METHOD
复制标题
DOI：
10.1002/nme.1620121010
复制
发表时间：
1978-01-01
影响因子：
2.9
通讯作者：
RHEINBOLDT, WC
中科院分区：
文献类型：
--
作者：
BABUSKA, I;RHEINBOLDT, WC
有限元解的可计算后验误差估计是在h → 0的渐近形式中导出的，其中h是单元尺寸的度量。该方法与残量法有相似之处，但与残量法的不同之处在于使用了与给定双线性（能量）形式相对应的负索伯列夫空间的范数。为了清楚起见，本演示仅限于一维模型问题。更具体地说，源，本征值和抛物问题被认为涉及一个线性，自伴算子的二阶。推广到更一般的一维问题是简单的，结果也扩展到更高的空间维度;但这涉及一些额外的考虑。该估计可用于计算有限元解的准确性的实际后验评估，并且它们为自适应有限元解算器的设计提供了基础。
Computablea‐posteriorierror estimates for finite element solutions are derived in an asymptotic form forh→ 0 wherehmeasures the size of the elements. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one‐dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self‐adjoint operator of the second order. Generalizations to more general one‐dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practicala‐posterioriassessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.