Adaptive Moving Mesh Methods

A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

“…A moving finite difference method based on a moving mesh PDE (MMPDE) [29,30] is used for the numerical study of IBVP (1.1)-(1.3). With the method, a mesh of J + 1 points,…”

“…The choice of M and τ has been discussed extensively in the literature, e.g., see [30,34]. In our computation, we take τ = 10 −2 and…”

“…In our computation, the monitor function is smoothed using ten sweeps of a low-pass filter (cf. [30]). …”

Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations

“…One is the Eulerian method [1][2][3][4] for which the fixed mesh is employed, when the length of the shock wave is similar to the length of the mesh, the accuracy will diminish significantly. In contrast, the other method: the Lagrangian (adaptive) method [5,6] is more efficient. In this case, the mesh is moved adaptively and always concentrated in regions with large and rapid variations.…”

“…The original PDE and the moving mesh equation form a coupled system and are often solved simultaneously by various numerical methods. Since the moving element methods by Miller et al [7] and the moving finite methods by Dorfi et al [8], the moving mesh method have been under extensive study, for details we refer the reader to [6,[9][10][11][12][13][14][15][16][17][18][19][20][21] and the references therein.…”