An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave Equation

Patrick Joly; Jerónimo Rodríguez

doi:10.1137/040603437

An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave Equation

Patrick Joly
, Jerónimo Rodríguez

INRIA Rocquencourt

Research output: Contribution to journal › Article › peer-review

Abstract

We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221]. The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L² convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].

Original language	English
Pages (from-to)	825-859
Number of pages	35
Journal	SIAM Journal on Numerical Analysis
Volume	43
Issue number	2
DOIs	https://doi.org/10.1137/040603437
Publication status	Published - 1 Dec 2005
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

Energy conservation
Error estimates
Local time stepping
Mesh refinement
Stability
Wave equation

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10.1137/040603437

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title = "An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave Equation",

abstract = "We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221]. The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].",

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AU - Joly, Patrick

AU - Rodríguez, Jerónimo

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N2 - We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221]. The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].

AB - We study two space-time mesh refinement methods as the one introduced in [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 197-221]. The stability of such methods is guaranteed by construction through the conservation of a discrete energy. In this paper, we show the L2 convergence of these schemes and provide optimal error estimates. The proof is based on energy techniques and bootstrap arguments. Our results are validated with numerical simulations and compared with results from plane wave analysis [F. Collino, T. Fouquet, and P. Joly, Numer. Math., 95 (2003), pp. 223-251].

KW - Energy conservation

KW - Error estimates

KW - Local time stepping

KW - Mesh refinement

KW - Stability

KW - Wave equation

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 2

ER -

An error analysis of conservative space-time mesh refinement methods for the one-dimensional wave Equation

Abstract

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Keywords

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