# Finite element interpolation error bounds with applications to eigenvalue problems

• Peter Arbenz
Original Papers

## Abstract

Optimal finite element interpolation eror bounds are presented for piecewise linear, quadratic and Hermite-cubic elements in one dimenson. These bounds can be used to compute upper and lower bounds for eigenvalues of second and fourth order elliptic problems. Numerical computations demonstrate the usefulness of the theoretical results.

## Keywords

Lower Bound Numerical Computation Theoretical Result Mathematical Method Eigenvalue Problem
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## Zusammenfassung

Es werden optimale Fehlerschranken für die eindimensionale finite Element-Interpolation mit stückweise linearen, quadratischen und Hermite-kubischen Elementen angegeben. Diese Schranken können dazu verwendet werden, unter und obere Schranken für Eigenwerte von elliptischen Problemen 2. und 4. Ordnung zu berechnen. Dazu werden numerische Resultate angeführt, welche die Nützlichkeit der theoretischen Resultate zeigen.

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