Article history: Received 12 September 2013 Received in revised form 8 April 2014 Accepted 3 July 2014 Available online 15 July 2014

We develop in this paper some efficient algorithms which are essential to implementations of spectral methods on the sparse grid by Smolyak’s construction based on a nested quadrature. More precisely, we develop a fast algorithm for the discrete transform between the values at the sparse grid and the coefficients of expansion in a hierarchical basis; and by using the aforementioned fast transfo...

Abstract. In this paper we present a mixed local discontinuous Galerkin formulation for linear elasticity problems in the plane with Dirichlet boundary conditions. The approach follows previous dual-mixed methods and introduces the stress and strain tensors, and the rotation, as auxiliary unknowns. Next, we use suitable lifting operators to eliminate part of the unknowns of the corresponding di...

This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two three dimensions. In spatial discretization, we use piecewise polynomials of degrees $ k \ (k \geq 1), k-1 l (l = k-1; k) to approximate scalar function, flux variable interface trace respectively. full discretization method, apply a backward Euler scheme tempo...

Article history: Received 21 February 2012 Received in revised form 30 May 2012 Accepted 4 June 2012 Available online 16 June 2012

Article history: Received 27 March 2011 Accepted 3 May 2012 Available online 15 May 2012

We conduct discrete spectrum analyses for a selection of mixed discretization schemes for the Stokes eigenproblem. In particular, we consider the MINI element, the Crouzeix-Raviart element, the Marker-andCell scheme, the Taylor-Hood element, the Qk/Pk−1 element, the divergence-conforming discontinuous Galerkin method, and divergence-conforming B-splines. For each of these schemes, we compare th...