相关论文: $hp$-version $C^1$-continuous Petrov-Galerkin meth…
This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The approximation piecewise polynomial spaces we deal with are of…
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…
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…
We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36,…
In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…
Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximation is challenging because the variable-order fractional…
An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the numerical scheme for the quad-curl equation and then derive…
In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori estimate for the turning point problem with a single boundary turning…
This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in the two and three dimensions. It is…
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…
A discontinuous Petrov-Galerkin (DPG) method is used to solve the time-harmonic equations of linear viscoelasticity. It is based on a "broken" primal variational formulation, which is very similar to the classical primal variational…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
We consider a control constrained parabolic optimal control problem and use variational discretization for its time semi-discretization. The state equation is treated with a Petrov-Galerkin scheme using a piecewise constant Ansatz for the…
Petrov-Galerkin methods are always considered in numerical solutions of differential and integral equations $ Ax=b $. It is common to consider the convergence and error analysis when $ b \in \mathcal{R}(A) $ which make the equation…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
Some properties of a Local discontinuous Galerkin (LDG) algorithm are demonstrated for the problem of evaluting a second derivative $g = f_{xx}$ for a given $f$. (This is a somewhat unusual problem, but it is useful for understanding the…
This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…
This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary…
We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size ($h$-method), we achieve accuracy by increasing the order of the method…