钟柳强, 李莹, 刘春梅. 非对称不定椭圆方程的两网格内罚间断有限元方法[J]. 华南师范大学学报（自然科学版）, 2016, 48(3): 7-13. DOI: 10.6054/j.jscnun.2016.03.026
引用本文: 钟柳强, 李莹, 刘春梅. 非对称不定椭圆方程的两网格内罚间断有限元方法[J]. 华南师范大学学报（自然科学版）, 2016, 48(3): 7-13. DOI: 10.6054/j.jscnun.2016.03.026
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ZHONG Liuqiang, LI Ying, LIU Chunmei. Two-Grid IPDG Method for Non-Symmetric Indefinite Elliptic Equations[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(3): 7-13. DOI: 10.6054/j.jscnun.2016.03.026
Citation: ZHONG Liuqiang, LI Ying, LIU Chunmei. Two-Grid IPDG Method for Non-Symmetric Indefinite Elliptic Equations[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(3): 7-13. DOI: 10.6054/j.jscnun.2016.03.026
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非对称不定椭圆方程的两网格内罚间断有限元方法

Two-Grid IPDG Method for Non-Symmetric Indefinite Elliptic Equations

    摘要
  • 摘要: 针对一类非对称或不定椭圆方程的内罚间断有限元方法,设计和分析了相应的两网格求解算法.首先给出了内罚间断有限元解的适定性,及其在L2和间断H1范数下的先验估计;其次设计了相应的两网格求解算法,并给出算法的误差分析;最后,数值实验结果验证了算法的高效性.

     

    Abstract: A two-grid interior penalty discontious Galkerkin (IPDG) method for non-symmetric indefinite elliptic equations is proposed. Firstly, the well-posedness of IPDG method and the optimal error estimates in both L2 norm and discontinuous H1 norm are proved. Then, the corresponding two-grid method is designed and the error estimate of the algorithm is provided. At last, the efficiency of the algorithm is validated by numerical experiments.

     

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