منابع مشابه
Balanced Monitoring of Flow Phenomena in Moving Mesh Methods
Adaptive moving mesh research usually focuses either on analytical derivations for prescribed solutions or on pragmatic solvers with challenging physical applications. In the latter case, the monitor functions that steer mesh adaptation are often defined in an ad-hoc way. In this paper we generalize our previously used monitor function to a balanced sum of any number of monitor components. This...
متن کاملMoving Mesh Methods Based on Moving
Several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh PDEs derived in a previous paper. These versions are quite simple and easy to program. They are applied to three benchmark one-dimensional problems which show diierent solution behaviour. The numerical results clearly demonstrate that the present methods are capable of accur...
متن کاملMoving Mesh Methods in Multiple DimensionsBased on Harmonic Maps
In practice, there are three types of adaptive methods using the finite element approach, namely the h-method, p-method, and r-method. In the h-method, the overall method contains two parts, a solution algorithm and a mesh selection algorithm. These two parts are independent of each other in the sense that the change of the PDEs will affect the first part only. However, in some of the existing ...
متن کاملMoving Mesh Finite Element Methods Based on Harmonic Maps
This paper is devoted to the applications of a class of moving mesh nite element methods based on harmonic maps. We review some recent work of the authors on solving PDES, variational inequalities and optimal control problems by use of the moving mesh techniques.
متن کاملMesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods
Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when mo...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.09.041