An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics

Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension

In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method with a time-dependent approximation space for one dimensional conservation laws, which satisfies the geometric conservation law. For the semi-discrete ALE-DG method, when applied to nonlinear scalar conservation laws, a cell entropy inequality, L2 stability and error estimates are prove...

A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media

An Arbitrary Lagrangian-Eulerian Local Discontinuous Galerkin Method for Hamilton-Jacobi Equations

Abstract: In this paper, an arbitrary Lagrangian-Eulerian local discontinuous Galerkin (ALE-LDG) method for Hamilton-Jacobi equations will be developed, analyzed and numerically tested. This method is based on the time-dependent approximation space defined on the moving mesh. A priori error estimates will be stated with respect to the $\mathrm{L}^{\infty}\left(0,T;\mathrm{L}^{2}\left(\Omega\rig...

An Efficient Eulerian-Lagrangian Method for Solving Solute Transport Problems in Steady and Transient Flow Fields

A computationally efficient, yet relatively simple Eulerian-Lagrangian method is proposed for solving the one-dimensional convection-dispersion solute transport equation assuming a steady or transient velocity field. The method uses a modified single-step reverse particle tracking (MSRPT) technique to handle steep concentration fronts. The scheme utilizes two weighting factors to control the mo...

An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems

In this article an unfitted Discontinuous Galerkin Method is proposed to discretize elliptic interface problems. The method is based on the Symmetric Interior Penalty Discontinuous Galerkin Method and can also be interpreted as a generalization of the method given in [A. Hansbo, P. Hansbo, An unfitted finite element method based on Nitsche’s method for elliptic interface problems, Comp. Meth. A...