非线性波动方程爆破解的不连续伽辽金法

IF 0.8 4区数学 Q2 MATHEMATICS

Turkish Journal of Mathematics Pub Date : 2023-01-01 DOI:10.55730/1300-0098.3408

Asma Azaiez, M. Benjemaa, Aida Jrajria, H. Zaag

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引用次数: 1

摘要

我们发展和研究了一种显式时空离散不连续伽辽金有限元法来近似一维非线性波动方程的解。我们证明了当考虑非均匀时间网格时，数值格式是稳定的。研究了爆破现象，证明了在弱收敛假设下，数值爆破时间趋向于理论爆破时间。通过几个实例和基准验证了我们结果的有效性

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Discontinuous Galerkin method for blow-up solutions of nonlinear wave equations

: We develop and study an explicit time-space discrete discontinuous Galerkin finite element method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several examples and benchmarks

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来源期刊

Turkish Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

161

审稿时长

6-12 weeks

期刊介绍： The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics. Contribution is open to researchers of all nationalities.