A POSTERIORI ERROR ESTIMATOR FOR OBSTACLE PROBLEMS

作者：Weiss Alexander^*; Wohlmuth Barbara I

来源：SIAM Journal on Scientific Computing, 2010, 32(5): 2627-2658.

DOI：10.1137/090773921

• equilibrated fluxes
• Lagrange multipliers
• a posteriori error estimates
• variational inequality
• obstacle problem
• H(div)-conforming lifting

In this paper, we consider a posteriori error estimators for obstacle problems. The variational inequality is reformulated as a mixed problem in terms of a discrete nodewise defined but variationally consistent Lagrange multiplier. Locally defined equilibrated fluxes and an H(div)-conforming lifting define our estimator. To obtain a better local upper bound for the estimator, we introduce a different elementwise defined Lagrange multiplier. Although the upper and lower bounds are established for affine obstacles, we present generalizations to nonsmooth obstacles and to non-matching meshes. Different numerical examples show the efficiency and reliability of our estimator. Due to its flexible construction principle and abstract framework, it can be also applied as an error indicator to more complex obstacle problems such as, e. g., American option pricing in financial mathematics.

• 出版日期2010