J
Joseph E. Flaherty
Researcher at Rensselaer Polytechnic Institute
Publications - 119
Citations - 5075
Joseph E. Flaherty is an academic researcher from Rensselaer Polytechnic Institute. The author has contributed to research in topics: Finite element method & Mesh generation. The author has an hindex of 41, co-authored 119 publications receiving 4864 citations. Previous affiliations of Joseph E. Flaherty include United States Department of the Army & University of Utah.
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Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
TL;DR: By detecting discontinuities in such variables as density or entropy, limiting may be applied only in these regions; thereby, preserving a high order of accuracy in regions where solutions are smooth.
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Parallel, adaptive finite element methods for conservation laws
TL;DR: This work constructs parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions and presents results using adaptive h- and p-refinement to reduce the computational cost of the method.
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A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
TL;DR: Convergence of local and global discretization errors to the Radau polynomial of degree p +1 holds for smooth solutions as p →∞ and is used to construct asymptotically correct a posteriori estimates of spatial discretized errors that are effective for linear and nonlinear conservation laws in regions where solutions are smooth.
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Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws
Joseph E. Flaherty,R. M. Loy,Mark S. Shephard,Boleslaw K. Szymanski,James D. Teresco,Louis H. Ziantz +5 more
TL;DR: To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size and processor load imbalances are corrected by using traversals of an octree representing a spatial decomposition of the domain.
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An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems
TL;DR: A high-order formulation for solving hyperbolic conservation laws using the discontinuous Galerkin method (DGM) is presented and an orthogonal basis for the spatial discretization is introduced and use explicit Runge--Kutta time discretized.