This paper investigates the use of a special class of strong-stability-preserving (SSP) Runge–Kutta time discretization methods in conjunction with discontinuous Galerkin (DG) finite element spatial discretizatons. The class of SSP methods investigated here is defined by the property that the number of stages s is greater than the order k of the method. From analysis, CFL conditions for the lin...

A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions ...

A stochastic element-free Galerkin method was developed for reliability analysis of linear-elastic structures with spatially varying random material properties. A random ®eld representing material properties was discretized into a set of random variables with statistical properties obtained from the statistical properties of random ®eld. In conjunction with meshless formulations, the ®rst-order...

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact ni...

In this paper, we present a new numerical method, the Immersed Element-Free Galerkin Method (IEFGM), for the solution of fluid-structure interaction problems. The technique is a variation of the Immersed Finite Element Method developed by (L. Zhang et al., Journal of Fluids and Structures, 23(6):836-857 (2007)) in which the fluid-solid interaction force is represented as a volumetric force in t...

We investigate a macro-element variant of the hybridized discontinuous Galerkin (HDG) method, using patches standard simplicial elements that can have non-matching interfaces. Coupled via HDG technique, our method enables local refinement by uniform subdivision each macro-element. By enforcing one spatial discretization for all macro-elements, we arrive at problems per are embarrassingly parall...