ADAPTIVE FINITE ELEMENT SIMULATION OF INCOMPRESSIBLE FLOWS BY HYBRID CONTINUOUS-DISCONTINUOUS GALERKIN FORMULATIONS

作者：Badia Santiago^*; Baiges Joan

来源：SIAM Journal on Scientific Computing, 2013, 35(1): A491-A516.

DOI：10.1137/120880732

• incompressible flows
• adaptive refinement
• continuous-discontinuous Galerkin
• equal-order interpolation
• stabilization

In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes. Then we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPG-type continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use a standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm for both uniformly and adaptively refined nonconforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.

• 出版日期2013