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

Mathematical Modelling and Analysis. 2018. Vol. 23. No. 3. P. 359–378.

Zlotnik A., Kireeva O.

We deal with the standard three-level bilinear FEM and finite-difference scheme to solve the initial-boundary value problem for the 1D wave equation. We consider initial data and the free term which are the Dirac delta-functions, discontinuous, continuous but with discontinuous derivatives and from the Sobolev spaces, accomplish the practical error analysis in the $L^2$, $L^1$, energy and uniform norms as the mesh refines and compare results with known theoretical error bounds.

Keywords: practical error analysis, практический анализ погрешности, разностная схема, finite-difference scheme, 1D wave equation, non-smooth data, bilinear finite element method, одномерное волновое уравнение, негладкие данные, билинейный метод конечных элементов

Publication based on the results of: Анализ погрешности численных методов решения задач математической физики на классах данных (2016)