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Construction of L2-orthogonal elements of arbitrary order for Local Projection Stabilization

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  • Schieweck, F.
  • Skrzypacz, P.
  • Tobiska, L.

Abstract

We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.

Suggested Citation

  • Schieweck, F. & Skrzypacz, P. & Tobiska, L., 2018. "Construction of L2-orthogonal elements of arbitrary order for Local Projection Stabilization," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 87-101.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:87-101
    DOI: 10.1016/j.amc.2018.04.070
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    Keywords

    Local projection stabilization; L2-orthogonal elements;

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