A POSTERIORI ERROR ESTIMATION OF hp-dG FINITE ELEMENT METHODS FOR HIGHLY INDEFINITE HELMHOLTZ PROBLEMS

作者：Sauter S^*; Zech J

来源：SIAM Journal on Numerical Analysis, 2015, 53(5): 2414-2440.

DOI：10.1137/140973955

• Helmholtz equation at high wavenumber
• hp-finite elements
• a posteriori error estimation
• discontinuous Galerkin methods
• ultra-weak variational formulation

In this paper, we will consider an hp-finite elements discretization of a highly indefinite Helmholtz problem by some dG-formulation which is based on the ultra-weak variational formulation by Cessenat and Depres. We will introduce an a posteriori error estimator and derive reliability and efficiency estimates which are explicit with respect to the wavenumber and the discretization parameters h and p. In contrast to the conventional conforming finite element method for indefinite problems, the dG-formulation is unconditionally stable and the adaptive discretization process may start from a very coarse initial mesh. Numerical experiments will illustrate the efficiency and robustness of the method.

• 出版日期2015