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

Alexander Zlotnik; Olga Kireeva

doi:10.3846/mma.2018.022

DOI: https://doi.org/10.3846/mma.2018.022

Abstract

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.

Keyword : 1D wave equation, non-smooth data, bilinear FEM, finite-difference scheme, practical error analysis

How to Cite

Zlotnik, A., & Kireeva, O. (2018). 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, 23(3), 359-378. https://doi.org/10.3846/mma.2018.022

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Jun 14, 2018

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