Showing papers by "Joseph E. Flaherty published in 1992"
TL;DR: Adaptive mesh refinement techniques for two-dimensional systems of parabolic partial differential equations are described in this article, where solutions are calculated using Galerkin's method with a piecewise bilinear basis in space and backward Euler integration in time.
50 citations
TL;DR: The adaptive solution of parabolic partial differential systems in one and two space dimensions is considered by finite element procedures that automatically refine and coarsen computational meshes, vary the degree of the piecewise polynomial basis and, in one dimension, move the computational mesh.
47 citations
TL;DR: A reliable and accurate a posteriori error estimator for quadratic triangular and tetrahedral elements is presented and its application in an automated, adaptive finite element modelling system for elasticity problems demonstrates its ability to accurately estimate the error in the energy norm.
Abstract: A reliable and accurate a posteriori error estimator for quadratic triangular and tetrahedral elements is presented. Its application in an automated, adaptive finite element modelling system for elasticity problems demonstrates its ability to accurately estimate the error in the energy norm. A local version of this error estimator is also used to determine the multiple level h-refinement necessary to improve the finite element mesh.
38 citations
01 May 1992
TL;DR: Consider the adaptive solution of two-dimensional vector systems of hyperbolic and elliptic partial differential equations on shared-memory parallel computers and a variety of heuristic processor load balancing techniques and refinement strategies.
Abstract: : Consider the adaptive solution of two-dimensional vector systems of hyperbolic and elliptic partial differential equations on shared-memory parallel computers. Hyperbolic systems are approximated by an explicit finite volume technique and solved by a recursive local mesh refinement procedure on a tree- structured grid. Local refinement of the time steps and spatial cells of a coarse base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. Computational procedures that sequentially traverse the tree while processing solutions on each grid in parallel, that process solutions at the same tree level in parallel, and that dynamically assign processors to nodes of the tree have been developed and applied to an example. Computational results comparing a variety of heuristic processor load balancing techniques and refinement strategies are presented.
1 citations
06 Jan 1992
1 citations
01 Apr 1992
TL;DR: An adaptive mesh moving and refinement finite volume method to solve the transient Euler equations of compressible flow in one and two space dimensions indicates that local mesh refinement with and without mesh moving provide dramatic improvements in accuracy over uniform mesh solutions.
Abstract: : We use an adaptive mesh moving and refinement finite volume method to solve the transient Euler equations of compressible flow in one and two space dimensions. Numerical solutions are generated by a MacCormack scheme with Davis's artificial viscosity model. Richardson's extrapolation is used to calculate estimates of the local discretization error which can be used to control mesh motion and refinement. Questions regarding the optimal combination of adaptive strategies and the characterization of the initial mesh are investigated. Results indicate that local mesh refinement with and without mesh moving provide dramatic improvements in accuracy over uniform mesh solutions; that mesh motion provides good results on relatively fine initial meshes; that each problem has an optimal initial mesh and that it is more efficient to begin with a coarser than optimal mesh and refine rather than starting with too fine a mesh; and that a combination of both the adaptive strategies produced the most accurate solutions.