Related papers: An optimal method for high order mixed derivatives…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
We derive and analyze high order discontinuous Galerkin methods for second-order elliptic problems on implicitely defined surfaces in $\mathbb{R}^{3}$. This is done by carefully adapting the unified discontinuous Galerkin framework of…
A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without…
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…
We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8, 9, 19, 21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by the weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
This paper considers the $ p $ ($ p=1,2,3 $) order numerical differentiation on function $ y $ in $ (0,2\pi) $. They are transformed into corresponding Fredholm integral equation of the first kind. Computational schemes with analytic…