Moving mesh methods for problems with blow-up
Nettet15. sep. 2005 · In certain cases the system develops a blow-up singularity in finite time. Fixed mesh methods are not well suited to approximate the problem near the singularity. As an alternative to reproduce the behaviour of the continuous solution, we present an adaptive in space procedure. Nettet20. okt. 2016 · To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation.
Moving mesh methods for problems with blow-up
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Nettetbe inefficient, we adopt moving mesh partial differential equation (MMPDE) method to adapt the spatial mesh as the singularity develops. Combining LABCs and MMPDE, … NettetThis paper studies the numerical solutions of semilinear parabolic partial differential equations (PDEs) on unbounded spatial domains whose solutions blow up in finite …
Nettet12. aug. 2014 · The mesh generator is based on minimizing the sum of two diagonal lengths in each cell. We also add second order difference terms to obtain smoother and … NettetWe consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs). Specifically, the underlying …
NettetThe choice of the discretization in time is made based on a careful analysis of adaptive time-stepping methods for ODEs that exhibit finite time blow-up. The new adaptive algorithm is shown to accurately estimate the blow-up time of a number of problems, including one which exhibits regional blow-up. MSC codes finite time blow-up NettetINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2004; 00:1–6 Prepared using fldauth.cls [Version: 2002/09/18 v1.01] A Moving Mesh Finite Element Algorithm for Fluid Flow Problems with Moving Boundaries M. J. Baines1, M. E. Hubbard2,∗ and P. K. Jimack2
NettetWe consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs).Specifically, the underlying PDE …
NettetIt is shown that for suitable ones the MMPDE solution evolves towards a (moving) mesh which close to the blow-up point automatically places the mesh points in such a manner that the ignition kernel, which is well known to be a natural coordinate in ... Keyphrases mesh method different choice dr chi auburn nyNettetWe consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs).Specifically, the underlying PDE and the MMPDE are solved for the blow-up solution and the computational mesh … end of the tax year ukNettetThe other essential difficulty is the character of blow-up in finite time. Since the singularity of blow-up contains large variations in small length scales, the numerical methods to reproduce such singularity behavior with uniform mesh diminish its accuracy significantly. The moving mesh partial differential equations (MMPDEs) method has end of the toriesNettet15. jan. 2008 · In convection-diffusion problems a first-order upwind difference approximation is usually used on a locally refined mesh to get a wiggle free solution, … dr chia thye pohNettetWe consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs).Specifically, the underlying PDE and the MMPDE are solved for the blow-up solution … end of the tax year 2021NettetIn this paper we will examine a class of r-adaptive moving mesh methods for approximating those solutions of the parabolic equation ut = u+f(u); x 2 ˆ Rd; uj@ = 0: (1) which become singular (blow-up) in a nite time T. We will concentrate in our calculations on the case of d = 2, although the methods can in principle work in higher dimensions. dr chia wen lee quincy maNettetThe work continues a series of articles devoted to the peculiarities of solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection-type with data on the position of the reaction front. In this paper, we place the emphasis on some problems of the numerical solving process. One of the approaches … dr. chia wong