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Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms,… (More)

Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without compromising simulation stability. Lately, another property of DG has been growing in importance: The… (More)

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The… (More)

- J. S. HESTHAVEN
- 1998

The electrostatic interpretation of the Jacobi-Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions deened on a simplex. Moreover, several new estimates, based on extensive numerical studies, for approximation along the line using Jacobi-Gauss-Lobatto quadrature points as the nodal sets are… (More)

This paper, concluding the trilogy, develops schemes for the stable solution of wave-dominated unsteady problems in general three-dimensional domains. The schemes utilize a spectral approximation in each sub-domain and asymptotic stability of the semi-discrete schemes is established. The complex computational domains are constructed by using non-overlapping… (More)

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equations defined on the tetrahedron. In the first part the question of well-behaved multivariate… (More)

Dedicated to our friend and mentor, Prof David Gottlieb, on the occasion of his 60 th birthday We discuss the use of Padé-Legendre interpolants as an approach for the postprocessing of data contaminated by Gibbs oscillations. A fast interpolation based reconstruction is proposed and its excellent performance illustrated on several problems. Almost… (More)

We introduce the Reduced Basis Method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized Electric Field Integral Equation (EFIE). This combination enables an algorithmic cooperation which results… (More)

We develop and evaluate a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical… (More)

We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. This approximation then defines a sur-rogate posterior probability density… (More)