We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinu-ities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting… (More)
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting… (More)
We examine the quality of partitions produced by an iterative load balancer in parallel adaptive finite element calculations. We present several metrics which we use to evaluate the quality of a mesh partitioning, and report statistics generated from our analysis of adaptively refined meshes produced during the solution of computational fluid dynamics… (More)
We describe a hierarchical basis for the p-version of the nite element method in two and three dimensions. The corresponding stiiness matrices are shown to have goodsparsity properties and better conditioning than those generated from existing hierarchical bases.
Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is… (More)
Data partitioning and load balancing are important components of parallel computations. Many different partitioning strategies have been developed, with great effectiveness in parallel applications. But the load-balancing problem is not yet solved completely; new applications and architectures require new partitioning features. Existing algorithms must be… (More)
An adaptive technique for a partial diierential system automatically adjusts a computational mesh or varies the order of a numerical procedure to obtain a solution satisfying prescribed accuracy criteria in an optimal fashion. We describe data structures for distributed storage of nite element mesh data as well as software for mesh adaptation, load… (More)
We present a high-order formulation for solving hyperbolic conservation laws using the Discon-tinuous Galerkin Method (DGM). We introduce an orthogonal basis for the spatial discretization and use explicit Runge-Kutta time discretization. Some results of higher-order adaptive refinement calculations are presented for in-viscid Rayleigh Taylor flow… (More)