A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation View Full Text


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Article Info

DATE

2019-12

AUTHORS

Junjun Wang, Lijuan Guo

ABSTRACT

We study a new way to convergence results for a nonlinear hyperbolic equation with bilinear element. Such equation is transformed into a parabolic system by setting the original solution u as ut=q. A linearized backward Euler finite element method (FEM) is introduced, and the splitting skill is exploited to get rid of the restriction on the ratio between h and τ. The boundedness of the solutions about the time-discrete system in H2-norm is proved skillfully through temporal error. The spatial error is derived without the mesh-ratio, where some new techniques are utilized to deal with the problems caused by the new parabolic system. The final unconditional optimal error results of u and q are deduced at the same time. Finally, a numerical example is provided to support the theoretical analysis. Here h is the subdivision parameter, and τ is the time step. More... »

PAGES

48

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13661-019-1161-9

DOI

http://dx.doi.org/10.1186/s13661-019-1161-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112527731


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