A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions
A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions
We consider a two dimensional biharmonic problem and its discretization by means of a symmetric interior penalty discontinuous Galerkin method. Based on the ``div-div'' complex, a novel split of an error measure based on a generalized Hessian into two terms measuring the conformity and nonconformity of the scheme is proven. This splitting is the departing point for the design of a new reliable and efficient error estimator, which does not involve any DG stabilization. Such an error estimator can be bounded from above by the standard DG residual error estimator. Numerical results assess the theoretical predictions, including the efficiency of the proposed estimator.
Théophile Chaumont-Frelet、Joscha Gedicke、Lorenzo Mascotto
数学
Théophile Chaumont-Frelet,Joscha Gedicke,Lorenzo Mascotto.A generalized Hessian-based error estimator for an IPDG formulation of the biharmonic problem in two dimensions[EB/OL].(2025-07-08)[2025-07-23].https://arxiv.org/abs/2507.05776.点此复制
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