We develop error estimates for the finite element approximation of elliptic partial differential equations on perturbed domains, i.e. when the computational domain does not match the real geometry. The result shows that the error related to the domain can be a dominating factor in the finite element discretization error. The main result consists of \(H^1\)- and \(L^2\)-error estimates for the Laplace problem. Theoretical considerations are validated by a computational example.

中文翻译：

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几何扰动域上的有限元误差估计

我们为扰动域上（即，当计算域与实际几何不匹配时）的椭圆偏微分方程的有限元逼近开发误差估计。结果表明，与域有关的误差可能是有限元离散化误差中的主要因素。主要结果包括\（H ^ 1 \） -和\（L ^ 2 \） -拉普拉斯问题的误差估计。理论上的考虑通过一个计算实例得到验证。