<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has become a research hotspot of many mathematicians. In fact, when describing practical physical problems with PDEs, non-linear problems tend to be more general than linear problems, which are close to real problems and have practical physical significance. Hyperbolic PDEs are a kind of important PDEs describing the phenomena of vibration or wave motion. The solution of hyperbolic PDE can be decomposed into the form of multiplication of vibration and vibration or of exponential function and exponential function. Generally, the energy is infinite. A full discrete convergence analysis method for non-linear hyperbolic equation based on finite element analysis is proposed. Taking second-order and fourth-order non-linear hyperbolic equation as examples, the full discrete convergence of non-linear hyperbolic equation is analysed by finite element method and the super-convergence results are obtained.</p>
</abstract>

With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has become a research hotspot of many mathematicians. In fact, when describing practical physical problems with PDEs, non-linear problems tend to be more general than linear problems, which are close to real problems and have practical physical significance. Hyperbolic PDEs are a kind of important PDEs describing the phenomena of vibration or wave motion. The solution of hyperbolic PDE can be decomposed into the form of multiplication of vibration and vibration or of exponential function and exponential function. Generally, the energy is infinite. A full discrete convergence analysis method for non-linear hyperbolic equation based on finite element analysis is proposed. Taking second-order and fourth-order non-linear hyperbolic equation as examples, the full discrete convergence of non-linear hyperbolic equation is analysed by finite element method and the super-convergence results are obtained.

Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 Public License.

With the development of modern partial differential equation (PDE) theory, the theory of linear PDE is becoming more and more perfect, . Non-linear PDE has...

Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Published Online: Nov 08, 2019

Page range: 433 - 444

Received: Sep 30, 2019

Accepted: Oct 15, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00041

Keywords
finite element analysis, nonlinearity, hyperbolic equation, fully discrete, convergence, error

© 2019 Qingli Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis

Published Online: Nov 08, 2019

Page range: 433 - 444

Received: Sep 30, 2019

Accepted: Oct 15, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00041

Keywordsfinite element analysis, nonlinearity, hyperbolic equation, fully discrete, convergence, error

© 2019 Qingli Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Keywords
finite element analysis, nonlinearity, hyperbolic equation, fully discrete, convergence, error