Abstract

High-order (HO) methods are of concerted academic and industrial interest in recent years due to their improved accuracy and their capability to deal with complex geometries [1]. Of particular note is the flux reconstruction method [2], which unifies several existing HO schemes into [...]

Abstract

This article presents a new methodology to compute numerical dispersion error. The analysis here presented is not restricted to uniform structured meshes nor linear discrete operators as it does not rely on sinusoids to compute the associated error. When using uniform meshes, the [...]

Abstract

This work describes the computational cost and accuracy of high-order numerical schemes on a simplified concept of multiple reference frame (MRF) technique using mixedelement unstructured grid framework widely tested for aerospace applications. The Reynolds averaged Navier-Stokes [...]

Abstract

This work presents a ZZ-BD a posteriori error estimator tailored for 3-D linear elastic fracture mechanics problems that are approximated by second-order pFEM-GFEM formulations. The proposed error estimator [...]

Abstract

GmshFem is an open source C++ finite element library based on the application programming interface of Gmsh. Both share the same design philosophy: to be fast, light and user-friendly. This paper presents the main principles of GmshFem, as well as some scalability results for high-order [...]

Abstract

This talk will present a method for achieving arbitrarily high orders of accuracy when approximating PDE-based moving boundary problems using finite element (and related) methods on moving computational meshes. Its effectiveness will be demonstrated on a nonlinear diffusion problem [...]

Abstract

We present an extension of the recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws. Using the method of lines, our schemes can handle unsteady flows with moving shocks, using time-accurate [...]