Abstract
This paper proposes moving mesh strategies for the moving mesh methods when solving the nonlinear time dependent partial differential equations (PDEs). Firstly we analyse Huang’s moving mesh PDEs (MMPDEs) and observe that, after Euler discretion they could be taken as one step of the root searching iteration methods. We improve Huang’s MMPDE by adding one Lagrange speed term. The proposed moving mesh PDE could draw the mesh to equidistribution quickly and stably. The numerical algorithm for the coupled system of the original PDE and the moving mesh equation is proposed and the computational experiments are given to illustrate the validity of the new method.
Highlights
For the numerical solution of nonlinear partial differential equations (PDEs) which involve large solution variations, large curvatures and even shock waves, two kinds of methods are generally considered
We show the approach through an example, and it can be generalized to various other kinds of the time dependent propagations problems
Proposed by Wu, and the present (18), one can observe that the proposed moving mesh equation includes both the advantages of the moving mesh PDEs (MMPDEs) proposed by Huang and Wu
Summary
For the numerical solution of nonlinear partial differential equations (PDEs) which involve large solution variations, large curvatures and even shock waves, two kinds of methods are generally considered. The original PDE and the moving mesh equation form a coupled system and are often solved simultaneously by various numerical methods. After Euler discretization on time, the MMPDEs could be taken as deformations of iteration methods on EP Based on this new explanation, the convergence conditions and orders on fixed time could be obtained. Combining the location based method by Huang and velocity based method by Wu, we construct the moving mesh PDEs in which the mesh are moved by two steps: firstly the approximation to the EP on fixed time, the movement along the character line of the original PDE to keep the distribution. The moving mesh PDE and the original PDE form a coupled PDE system [9] In this manuscript, the PDE system is simulated simultaneously by methods of line.
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