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A Conservative and ...
A Conservative and Energy Stable Ddiscontinuous Spectral Element Method for The Shifted WaveEquation in Second Order Form
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- Duru, Kenneth (author)
- Mathematical Sciences Institute, Australian National University, ACT, Canberra, Australia
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- Wang, Siyang (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Wiratama, Kenny (author)
- Mathematical Sciences Institute, Australian National University, ACT, Canberra, Australia
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(creator_code:org_t)
- Philadephia : Siam Publications, 2022
- 2022
- English.
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In: SIAM Journal on Numerical Analysis. - Philadephia : Siam Publications. - 0036-1429 .- 1095-7170. ; 60:4, s. 1631-1664
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of the following very successful numerical techniques: the summation-by-parts finite difference method, the spectral method, and the discontinuous Galerkin method. We prove energy stability and the discrete conservation principle and derive error estimates in the energy norm for the (1+1)-dimensions shifted wave equation in second order form. The energy-stability results, discrete conservation principle, and the error estimates generalize to multiple dimensions using tensor products of quadrilateral and hexahedral elements. Numerical experiments, in (1+1)-dimensions and (2+1)-dimensions, verify the theoretical results and demonstrate optimal convergence of L2 numerical errors at subsonic, sonic and supersonic regimes.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- constraint preserving
- Einstein's equations
- second order hyperbolic PDE
- shifted wave equation
- spectral element method
- stability
Publication and Content Type
- ref (subject category)
- art (subject category)
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