Velocity-Based Adaptive Methods
In this chapter we discuss velocity-based adaptive moving mesh methods. Although the classification of methods as being either velocity-based or location-based can at times be somewhat artificial, the former are generally characterized by the fact that their formulations directly target the mesh velocity, with the subsequent mesh points determined by integrating the velocity field. Some of these methods are motivated by the Lagrangian method in computational fluid dynamics (e.g., see Fletcher  or §7.1.1) and some others are based on minimizing a quantity related to error. A fortuitous property of the Lagrangian methods is that it is well-suited to maintaining sharper material interfaces since convection terms are eliminated from the governing equations. A disadvantage is that the meshes have a tendency to tangle and lose spatial resolution of the solution. Unfortunately, the Lagrangian-like moving mesh methods also inherit this disadvantage of Lagrangian methods, and major effort has gone into the development of these methods so as to avoid mesh tangling and/or regain spatial accuracy.
KeywordsMesh Point Lagrangian Method Adaptive Mesh Porous Medium Equation Mesh Equation
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