A Posteriori Error Estimates Based on the Polynomial Preserving Recovery

نویسندگان

  • Ahmed Naga
  • Zhimin Zhang
چکیده

Superconvergence of order O(h), for some ρ > 0, is established for the gradient recovered with the Polynomial Preserving Recovery (PPR) when the mesh is mildly structured. Consequently, the PPR-recovered gradient can be used in building an asymptotically exact a posteriori error estimator.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

متن کامل

Validation of the Quality of the A Posteriori Error Estimator Based on Polynomial Preserving Recovery for Linear Elements

In this paper the quality of the error estimator based on the Polynomial Preserving Recovery (PPR) is investigated using the computer-based approach described in [1, 3]. Also, a comparison is made between the performance of the error estimator based on the PPR and the one based on the Superconvergence Patch Recovery (SPR).

متن کامل

Polynomial Preserving Gradient Recovery and a Posteriori Estimate for Bilinear Element on Irregular Quadrilaterals

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h) for ρ = min(α, 1), when the mesh is distorted O(h) (α > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

متن کامل

A posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

متن کامل

Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?

~ We study. adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Second...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Numerical Analysis

دوره 42  شماره 

صفحات  -

تاریخ انتشار 2004