非对称不定椭圆方程的两网格内罚间断有限元方法

基金项目:

国家自然科学基金项目(11201159);全国博士学位论文作者专项资金项目(201212);广东省高等学校优秀青年教师培养计划专项(Yq2013054);湖南省自然科学基金项目(14JJ3135);广州市珠江科技新星项目(2013J2200063)

详细信息

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

1.
(1.School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China;
2.
2.College of Science,Hunan University of Science and Engineering,Yongzhou 425199,China)

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.
- 非对称不定椭圆方程 /
- 内罚间断有限元方法 /
- 两网格方法 /
- 误差估计
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.
- non-symmetric indefinite elliptic equation /
- interior penalty discontious Galkerkin method /
- two-grid method /
- error estimates