Publications

Weirs, Vincent G.; Lemke, Raymond W.; Robinson, Allen C.; Ober, Curtis C.; Banks, Jeffrey W.; Love, Edward L.; Scovazzi, Guglielmo S.; Shadid, John N.; Hanshaw, Heath L.

Abstract not provided.

Computer methods in applied mechanics and engineering

Scovazzi, Guglielmo S.; Love, Edward L.

Abstract not provided.

Computer Methods in Applied Mechanics and Engineering

Hughes, Thomas J.R.; Scovazzi, Guglielmo S.; Bochev, Pavel B.; Buffa, Annalisa

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees-of-freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations. © 2005 Elsevier B.V. All rights reserved.

Scovazzi, Guglielmo S.; Love, Edward L.; Love, Edward L.

A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to currently implemented hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical meaning, since it embeds a discrete form of the Clausius-Duhem inequality. Effectively, the proposed stabilization samples and acts to counter the production of entropy due to numerical instabilities. The proposed technique is applicable to materials with no shear strength, for which there exists a caloric equation of state. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method.

Scovazzi, Guglielmo S.; Bochev, Pavel B.; Collis, Samuel S.

Abstract not provided.

Scovazzi, Guglielmo S.; Bochev, Pavel B.

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees-of-freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations.

Scovazzi, Guglielmo S.

Abstract not provided.

Heinstein, Martin W.; Scovazzi, Guglielmo S.; Robinson, Allen C.

Abstract not provided.

Heinstein, Martin W.; Scovazzi, Guglielmo S.; Robinson, Allen C.

Abstract not provided.

Scovazzi, Guglielmo S.

We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components. Variational multiscale analysis is used to define an interscale transfer operator that associates coarse and fine scale functions. Composition of this operator with a donor DG method yields a new formulation that combines the advantages of DG methods with the attractive and more efficient computational structure of a continuous Galerkin method. The new class of DG methods is illustrated for a scalar advection-diffusion problem.

Scovazzi, Guglielmo S.; Bochev, Pavel B.

Abstract not provided.