We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The backward euler anisotropic a posteriori error analysis for parabolic integro-differential equations.
- Authors
Reddy, Gujji Murali Mohan; Sinha, Rajen Kumar
- Abstract
We derive two optimal a posteriori error estimators for an implicit fully discrete approximation to the solutions of linear integro-differential equations of the parabolic type. A continuous, piecewise linear finite element space is used for the space discretization and the time discretization is based on an implicit backward Euler method. The a posteriori error indicator corresponding to space discretization is derived using the anisotropic interpolation estimates in conjunction with a Zienkiewicz-Zhu error estimator to approach the error gradient. The error due to time discretization is derived using continuous, piecewise linear polynomial in time. We use the linear approximation of the Volterra integral term to estimate the quadrature error in the second estimator. Numerical experiments are performed on the isotropic mesh to validate the derived results.© 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1309-1330, 2016
- Subjects
EULER method; NUMERICAL solutions to integro-differential equations; NUMERICAL solutions to parabolic differential equations; DISCRETIZATION methods; NUMERICAL solutions to Voterra equations
- Publication
Numerical Methods for Partial Differential Equations, 2016, Vol 32, Issue 5, p1309
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22049