English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper addresses the properties of Continuous Interior Penalty (CIP)finite element solutions for the Helmholtz equation. The $h$-version of the CIPfinite element method with piecewise linear approximation is applied to aone-dimensional model problem. We first show discrete well posedness andconvergence results, using the imaginary part of the stabilization operator,for the complex Helmholtz equation. Then we consider a method with real valuedpenalty parameter and prove an error estimate of the discrete solution in the$H^1$-norm, as the sum of best approximation plus a pollution term that is theorder of the phase difference. It is proved that the pollution can beeliminated by selecting the penalty parameter appropriately. As a result ofthis analysis, thorough and rigorous understanding of the error behaviorthroughout the range of convergence is gained. Numerical results are presentedthat show sharpness of the error estimates and highlight some phenomena of thediscrete solution behavior.

Continuous Interior Penalty Finite Element Method for Helmholtz Equation with High Wave Number: One Dimensional Analysis