Research Report on the Hypercircle Method
نویسنده
چکیده
We got interested in the hypercircle method since it enables the derivation of reliable a posteriori error estimates without generic constants. It turned out, however, that it avoids also a loss of efficiency that we encounter when residual error estimators are used with the hp finite element method. Moreover, we obtain a priori error estimates for the comparison of different finite element families that are not achieved with the classical tools.
منابع مشابه
Local a Posteriori Error Estimator Based on the Hypercircle Method
The error of the finite element solution of linear elliptic problems can be estimated a posteriori by the classical hypercircle method. This method gives accurate and guaranteed upper bound of the error measured in the energy norm. The disadvantage is that a global dual problem has to be solved, which is quite time-consuming. Combining the hypercircle method with the equilibrated residual metho...
متن کاملDietrich Braess , Ronald H . W . Hoppe , and Joachim Schöberl A Posteriori Estimators for Obstacle Problems by the Hypercircle Method
A posteriori error estimates for the obstacle problem are established in the framework of the hypercircle method. To this end, we provide a general theorem of Prager– Synge type. There is now no generic constant in the main term of the estimate. Moreover, the role of edge terms is elucidated, and the analysis also applies to other types of a posteriori error estimators for obstacle problems.
متن کاملAn a posteriori error estimate and a Comparison Theorem for the nonconforming P 1 element
A posteriori error estimates for the nonconforming P1 element are easily determined by the hypercircle method via Marini’s observation on the relation to the mixed method of Raviart–Thomas. Another tool is Ainsworth’s application of the hypercircle method to mixed methods. The relation on the finite element solutions is also extended to an a priori relation of the errors, and the errors of four...
متن کاملA posteriori estimators for obstacle problems by the hypercircle method
A posteriori error estimates for the obstacle problem are established in the framework of the hypercircle method. To this end, we provide a general theorem of Prager– Synge type. There is now no generic constant in the main term of the estimate. Moreover, the role of edge terms is elucidated, and the analysis also applies to other types of a posteriori error estimators for obstacle problems.
متن کاملGuaranteed and locally computable a posteriori error estimate
A new approach, based on the combination of the equilibrated residual method and the method of hypercircle, is proposed for a posteriori error estimation. Computer implementation of the equilibrated residual method is fast, but it does not produce guaranteed estimates. On the other hand, the method of hypercircle delivers guaranteed estimates, but it is not fast because it involves solving a gl...
متن کامل