理科毕业论文外文翻译(编辑修改稿)

理科毕业论文外文翻译(编辑修改稿)内容摘要：

esults may be obtained by extra polation. The solutions of the toolbox equation often have geometric features like localized strong gradients. An example of engineering importance in elasticity is the stress concentration occurring at reentrant corners such as the MATLAB favorite, the Lshaped membrane. Then it is more economical to refine the mesh selectively, ., only where it is needed. When the selection is based ones timates of errors in the puted solutions, a posteriori estimates, we speak of adaptive mesh refinement. See adapt mesh for an example of the putational savings where global refinement needs more than 6000elements to pete with an adaptively refined mesh of 500 elements. The adaptive refinement generates a sequence of solutions on s uccessively finer meshes, at each stage selecting and refining those elements that are judged to contribute most to the error. The process is terminated when the maximum number of elements is exceeded or when each triangle contributes less than a preset tolerance. You need to provide an initial mesh, and choose selection and termination criteria parameters. The initial mesh can be produced by the init mesh function. The three ponents of the algorithm are the error indicator function, which putes an estimate of the element error contribution, the mesh refiner, which selects and subdivides elements, and the termination criteria. The Error Indicator Function The adaption is a feedback process. As such, it is easily applied to a lar gerrange of problems than those for which its design was tailored. You wantes timates, selection criteria, etc., to be optimal in the sense of giving the mostaccurate solution at fixed cost or lowest putational effort for a given accuracy. Such results have been proved only for model problems, butgenerally, the equid is tribution heuristic has been found near optimal. Element sizes should be chosen such that each element contributes the same to the error. The theory of adaptive schemes makes use of a priori bounds for solutions in terms of the source function f. For none lli ptic problems such abound may not exist, while the refinement scheme is still well defined and has been found to work well. The error indicator function used in the toolbox is an elementwise estimate of the contribution, based on the work of C. Johnson et al. For Poisson39。 sequation –f solution uhholds in the L2norm where h = h(x) is the local mesh size, and The braced quantity is the jump in normal derivative of v hr is the Ei, the set of all interior edges of the train gulation. This bound is turned into an elementwise error indicator function E(K) for element。