Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data

Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data

We deal with the standard three-level bilinear FEM and finite-difference scheme with a weight to solve the initial-boundary value problem for the 1D wave equation. We consider the rich collection of initial data and the free term which are the Dirac δ-functions, discontinuous, continuous but with di...

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Main Authors: Alexander Zlotnik, Olga Kireeva
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2018-06-01
Series:Mathematical Modelling and Analysis
Subjects:
1D wave equation
non-smooth data
bilinear FEM
finite-difference scheme
practical error analysis
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/2807
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spelling doaj-fe5676af43a24aa88d6689624e86a9ca2021-07-02T10:52:09ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102018-06-0123310.3846/mma.2018.022Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth dataAlexander Zlotnik0Olga Kireeva1National Research University Higher School of Economics, Myasnitskaya 20, 101000 Moscow, RussiaRussian State Social University, W. Pieck 4, 129226 Moscow, RussiaWe deal with the standard three-level bilinear FEM and finite-difference scheme with a weight to solve the initial-boundary value problem for the 1D wave equation. We consider the rich collection of initial data and the free term which are the Dirac δ-functions, discontinuous, continuous but with discontinuous derivatives and from the Sobolev spaces, accomplish the practical error analysis in the L2, L1, energy and uniform norms as the mesh refines and compare results with known theoretical error bounds. https://journals.vgtu.lt/index.php/MMA/article/view/28071D wave equationnon-smooth databilinear FEMfinite-difference schemepractical error analysis
collection DOAJ
language English
format Article
sources DOAJ
author Alexander Zlotnik
Olga Kireeva
spellingShingle Alexander Zlotnik
Olga Kireeva
Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
Mathematical Modelling and Analysis
1D wave equation
non-smooth data
bilinear FEM
finite-difference scheme
practical error analysis
author_facet Alexander Zlotnik
Olga Kireeva
author_sort Alexander Zlotnik
title Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
title_short Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
title_full Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
title_fullStr Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
title_full_unstemmed Practical error analysis for the three-level bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data
title_sort practical error analysis for the three-level bilinear fem and finite-difference scheme for the 1d wave equation with non-smooth data
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2018-06-01
description We deal with the standard three-level bilinear FEM and finite-difference scheme with a weight to solve the initial-boundary value problem for the 1D wave equation. We consider the rich collection of initial data and the free term which are the Dirac δ-functions, discontinuous, continuous but with discontinuous derivatives and from the Sobolev spaces, accomplish the practical error analysis in the L2, L1, energy and uniform norms as the mesh refines and compare results with known theoretical error bounds.
topic 1D wave equation
non-smooth data
bilinear FEM
finite-difference scheme
practical error analysis
url https://journals.vgtu.lt/index.php/MMA/article/view/2807
work_keys_str_mv AT alexanderzlotnik practicalerroranalysisforthethreelevelbilinearfemandfinitedifferenceschemeforthe1dwaveequationwithnonsmoothdata
AT olgakireeva practicalerroranalysisforthethreelevelbilinearfemandfinitedifferenceschemeforthe1dwaveequationwithnonsmoothdata
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