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 se...

Coupled two-dimensional (2D) morphodynamic and bank erosion models are gaining attentions in recent years. It has been shown that such models have advantages over the one-dimensional (1D) modeling approaches. In this paper, a previous 2D bank erosion model with the moving mesh method is extended to include the fixed mesh approach. Further, two practical streams with differing complexity are sim...

tion, which is often called a reaction–convection–diffusion equation, is representative of many problems which are It is well known that moving mesh and upwinding schemes are two kinds of techniques for tracking the shock or steep wave front solved by moving mesh methods in one dimension. in the solution of PDEs. It is expected that their combination should Much work has been devoted to the con...

A moving finite element-based inverse method for determining the temperature on a moving surface is developed. The moving mesh is generated employing the transfinite mapping technique. The proposed algorithms are used in the estimation of surface temperature on a moving boundary with high velocity in the burning process of a homogenous low thermal diffusivity solid fuel. The measurements obtain...