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Abstract We derive a residual-based a posteriori error estimator for the conforming hp -Adaptive Finite Element Method ( hp -AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classical h -version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [28] in the context of the hp -AFEM. Numerical experiments show the performance of an adaptive hp-FEM algorithm using the proposed a posteriori error estimator.
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This content will become publicly available on November 15, 2025
A posteriori error estimates of Darcy flows with Robin-type jump interface conditions
In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott-Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.
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- Award ID(s):
- 2110781
- PAR ID:
- 10645439
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Computers and mathematics with applications
- ISSN:
- 0898-1221
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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