ANALYSIS OF MOVING MESH METHODS BASED ON GEOMETRICAL VARIABLES

摘要

In this study we will consider moving mesh methods for solving one-dimensional time dependent PDEs. The solution and mesh are obtained simultaneously by solving a system of differential-algebraic equations. The differential equations involve the solution and the mesh, while the algebraic equations involve several geometrical variables such as θ (the) tangent angle), U (the normal velocity of the solution curve) and T(tangent velocity). The equal-arclength principle is employed to give a close form for T.