相关论文: The Bondi problem revisited: a spectral domain dec…

We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regularisation viewpoint of the wave equation in second-order…

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…

A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…

We propose a limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservation laws. Provided the scheme is discretely conservative and…

This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…

In this paper, we construct an efficient numerical scheme for full-potential electronic structure calculations of periodic systems. In this scheme, the computational domain is decomposed into a set of atomic spheres and an interstitial…

We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear…

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…

This paper studies Galerkin approximations applied to the Zakai equation of stochastic filtering. The basic idea of this approach is to project the infinite-dimensional Zakai equation onto some finite-dimensional subspace generated by…

A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…

Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lower-dimensional integrals. For that same reason, the matrix assembly…

In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…

Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…

This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…

In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts operators. To this end, it is crucial that structure preserving…

This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure…