Engineering Computations · 1993 · 15 citations · 9 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsEigenvalue ProblemsError EstimationFinite Element DiscretizationFinite Element FormulationNumerical AcousticsVibration AnalysisDiscretizationDiscretization ErrorDiscretization Error AnalysisEigenvalue Problems In AcousticsError Estimation For Eigenvalue ProblemsError Estimation For Finite Element SolutionsInterpolation FunctionsRayleigh Quotient
This paper presents a new approach for estimating the discretization error of finite element analysis of generalized eigenproblems. The method uses smoothed gradients at nodal points to derive improved element‐by‐element interpolation functions. The improved interpolation functions and their gradients are used in the Rayleigh quotient to obtain an improved eigenvalue. The improved eigenvalue is used to estimate the error of the original solution. The proposed method does not require any re‐solution of the eigenproblem. Results for 1‐D and 2‐D C° eigenproblems in acoustics and elastic vibrations are used as examples to demonstrate the accuracy of the proposed method.
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