A linearized spectral Galerkin/finite difference approach is developed for variable fractional-order nonlinear diffusion–reaction equations with a fixed time delay. The temporal discretization the variable-order fractional derivative performed by L1-approximation. An appropriate basis function in terms of Legendre polynomials used to construct Galerkin method spatial second-order operator. main...

The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier–Stokes equations. Optimal error estimates are derived for velocity in L2 norm time and space. Error bounds discrete derivative of also established. analysis challenging technical based on appropriate use lift operators duality arguments.

In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply compact finite difference method and interior penalty discontinuous Galerkin element to discretize space variable present two semi-discrete schemes, respectively. Then make use of discrete gradient Pad\'e ap...

In the implementation of boundary element methods for 3D elliptic PDEs in a given geometry there are two main numerical tasks: the stiiness matrix assembly and the solution of the resulting linear systems. The linear solve (performed directly) is O(n 3)-where n is the number of degrees of freedom-and is asymp-totically the most expensive component. Hence there are a number of modern techniques ...

In [20] a symmetric interior penalty discontinuous Galerkin (DG) method was presented for the time-dependent wave equation. In particular, optimal a-priori error bounds in the energy norm and the L-norm were derived for the semi-discrete formulation. Here the error analysis is extended to the fully discrete numerical scheme, when a centered second-order finite difference approximation (“leapfro...

Non-symmetric matrices may arise in the discretization of self-adjoint problems when a Petrov–Galerkin, collocation, or finite-volume method is employed. While these methods have been widely applied, this paper it shown that use non-symmetric incompatable with conservation energy elastodynamics. First, consistency between continuous forms momentum equation and examined. It linear equivalent to ...

The problem of constraint preservation for discretizations of nonlinear PDEs is addressed in the example of the hyperbolic Yang–Mills equations in temporal gauge. These equations preserve a nonlinear divergence field analogous to the electric charge for Maxwell’s equations. We introduce and discuss several discretizations of these equations on finite element spaces of Lie algebra valued differe...

We analyze the classical discontinuous Galerkin method for a general parabolic equation. Symmetric error estimates for schemes of arbitrary order are presented. The ideas we develop allow us to relax many assumptions freqently required in previous work. For example, we allow different discrete spaces to be used at each time step and do not require the spatial operator to be self adjoint or inde...

In this paper, an hp-local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On hp-quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates i...