الفهرس 
SummaryOnly 14 pages are availabe for public view
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Abstract
Integral equations (IEs) are considered one of the most prevalent equations in many engineering, physical and chemical fields. Approximate solutions to these equations are of great importance due to the limited availability of their exact solutions especially on complex domains. There are several methods used to obtain approximate solutions to IEs including finite element methods (FEMs). Researchers grew more interest in FEMs as a result of the progress in computer programs that greatly facilitated complicated mathematical operations required for applying these methods. In this thesis, we explored some techniques that improve the approximate solutions resulting from FEMs and study the potential contribution of these techniques in estimating the error in integral and integro- differential equations. The error estimation is an essential step to discover the regions in the finite element mesh where the errors exceeds the allowed limits. This helps in developing refinement algorithms to obtain solutions that are more accurate with minimal computational cost. We presented two approaches for evaluating a posteriori error estimates for such problems using the polynomial preserving recovery (PPR) technique and the supercovergent patch recovery (SPR) technique. Both PPR and SPR are techniques employed to improve the finite element solutions.