Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions

Any finite element analysis performed by an engineer is subject to several types of errors that can compromise the validity of the results. These errors can be broadly classified under the following categories: 1) user error - incorrect usage of FE software or input by the FE analyst, 2) errors due to assumptions and simplifications used in the model and 3) errors due to insufficient mesh discretization. User errors can be prevented by developing and utilizing a comprehensive pre and post processing checklist and by appropriate training in the basics of finite element analysis and usage of FE software. Errors due to modeling assumptions and simplifications can be alleviated by adding complexity to the model so that it better represents the physics of the problem being analyzed. Errors due to the inadequacy or coarseness of the mesh are often overlooked by the analyst. These errors due to mesh discretization can be fixed by evaluating the quality of the mesh and by developing and utilizing criteria that characterize the accuracy of the FE solution. This paper describes the source of mesh discretization error and presents several criteria that can be used by an FE analyst to evaluate the accuracy of the FE solution.
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