In this paper, we propose a new discontinuous Galerkin finite element method to solve the Hamilton–Jacobi equations. Unlike the discontinuous Galerkin method of [C. Hu, C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton–Jacobi equations, SIAM Journal on Scientific Computing 21 (1999) 666–690.] which applies the discontinuous Galerkin framework on the conservation law system ...

In this paper we present an a priori error estimate of the Runge-Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge-Kutta method and the finite element space is made up of piecewise polynomials of degree k ≥ 2. Quasi-optimal error estimate is obtained by energy techniques,...

We present a modified finite element method that is able to approximate interface problems with high accuracy. We consider interface problems, where the solution is continuous, its derivatives however may be discontinuous across interface curves within the domain. The proposed discretization is based on a local modification of the finite element basis which corresponds to a fitted finite elemen...

This paper studies the error in, the efficient implementation of and time stepping methods for a variational multiscale method (VMS) for solving convectiondominated problems. The VMS studied uses a fine mesh C 0 finite element space Xh to approximate the concentration and a coarse mesh discontinuous vector finite element space LH for the large scales of the flux in the two scale discretization....

This paper examines the development and implementation of second-order accurate non-reflecting boundary conditions in a time-discontinuous Galerkin finite element method for structural acoustics in unbounded domains. The formulation is based on a multi-field space-time variational equation for both the acoustic fluid and elastic solid together with their interaction. This approach to the modeli...

A finite element simulation framework for cutting and fracturing model without remeshing is presented. The main idea of proposed method is adding a discontinuous function for the standard approximation to account for the crack. A feasible technique is adopted for dealing with multiple cracks and intersecting cracks. Several involved problems including extended freedoms of finite element nodes a...