On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods

Numerical accuracy and efficiency of several discontinuous high-order methods, including the quadrature-based discontinuous Galerkin (QDG), nodal discontinuous Galerkin (NDG), spectral difference (SD) and flux reconstruction/correction procedure via reconstruction (FR/CPR), for the conservation laws are analyzed and compared on both linear and curved quadrilateral elements. On linear elements, all the above schemes are one-dimensional in each natural coordinate direction. However, on curved elements, not all schemes can be reduced to a one-dimensional form, although the SD and CPR formulations remain one-dimensional by design. The efficiency and accuracy of various formulations are compared on highly skewed curved elements. Several benchmark problems are simulated to further evaluate the performance of these schemes. (C) 2013 Elsevier Inc. All rights reserved.