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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Composite mesh concept based FEM error estimation and solution improvement
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Composite mesh concept based FEM error estimation and solution improvement

机译：基于复合网格概念的有限元误差估计和解决方案改进

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The use of composite finite element models where meshes with different granularities are allowed to share the same problem domain, is introduced. The idea of this method was taken from the mixture theory of multiphase materials, where the properties of each component enter into the formulation affected by a participation factor. The different behaviors of each component mesh due to differences in the model accuracy rather than to the material properties. We perform estimation of local and global errors for some problems in planar domains that are drawn from engineering problems (fractural elastic deformations or heat and mass transfer in catalytic chemical reactors). The main examples in this work are elliptic problems with boundary conditions of Dirichlet, Neumann, and mixed types. The method is not restricted to 2D, being also applicable to 3D problems. In this paper, we also develop the use of composite models with the target of improving the numerical solution of finite element models. By using extrapolation-like concepts, improved solutions may be obtained without increasing the computational cost of the problem or requiring postprocessing of the results. Some examples are shown for which exact solution is available in order to validate the method.
机译：介绍了复合有限元模型的使用，其中允许具有不同粒度的网格共享同一问题域。该方法的思想来自多相材料的混合理论，在该理论中，每种成分的特性均受参与因子影响而进入配方。由于模型精度而不是材料属性的差异，每个零部件网格的行为不同。我们对由工程问题（催化化学反应器中的断裂弹性变形或传热传质）引起的某些平面问题进行局部和全局误差估计。这项工作的主要例子是椭圆问题，其边界条件为Dirichlet，Neumann和混合类型。该方法不限于2D，也适用于3D问题。在本文中，我们还开发了复合模型的用途，目的是改进有限元模型的数值解。通过使用类似外推的概念，可以在不增加问题的计算成本或不需要对结果进行后处理的情况下获得改进的解决方案。显示了一些示例，其中提供了确切的解决方案以验证该方法。

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