Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
SIAM Journal on Scientific Computing
On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
An error indicator monitor function for an r-adaptive finite-element method
Journal of Computational Physics
Variational Barrier Method of Adaptive Grid Generation in Hyperbolic Problems of Gas Dynamics
SIAM Journal on Numerical Analysis
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
SIAM Journal on Control and Optimization
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
Journal of Computational Physics
Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
On Resistive MHD Models with Adaptive Moving Meshes
Journal of Scientific Computing
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In this paper, a moving mesh discontinuous Galerkin (DG) method is developed to solve the nonlinear conservation laws. In the mesh adaptation part, two issues have received much attention. One is about the construction of the monitor function which is used to guide the mesh redistribution. In this study, a heuristic posteriori error estimator is used in constructing the monitor function. The second issue is concerned with the solution interpolation which is used to interpolates the numerical solution from the old mesh to the updated mesh. This is done by using a scheme that mimics the DG method for linear conservation laws. Appropriate limiters are used on seriously distorted meshes generated by the moving mesh approach to suppress the numerical oscillations. Numerical results are provided to show the efficiency of the proposed moving mesh DG method.