Adaptive multilevel methods for obstacle problems
Adaptive multilevel methods for obstacle problems
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DOI：
10.1137/0731016
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发表时间：
1994-04
影响因子：
2.9
通讯作者：
R. Hoppe;R. Kornhuber
中科院分区：
文献类型：
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作者：
R. Hoppe;R. Kornhuber
作者考虑通过分段线性有限元对二阶椭圆微分算子的障碍问题进行离散化。假设通过合适的活动集策略将离散问题简化为一系列线性问题，通过预条件共轭梯度迭代来迭代求解线性问题。所提出的预处理器在理论上被视为抽象加性施瓦茨方法，并被实现为截断的分层基础预处理器。为了允许局部网格细化，导出半局部和局部后验误差估计，从而提供离散化误差的下限和上限估计。通过数值计算说明了理论结果。
The authors consider the discretization of obstacle problems for second-order elliptic differential operators by piecewise linear finite elements. Assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies, the linear problems are solved iteratively by preconditioned conjugate gradient iterations. The proposed preconditioners are treated theoretically as abstract additive Schwarz methods and are implemented as truncated hierarchical basis preconditioners. To allow for local mesh refinement semilocal and local a posteriors error estimates are derived, providing lower and upper estimates for the discretization error. The theoretical results are illustrated by numerical computations.