论文标题
关于自适应最小二乘有限元方法平原收敛的简短说明
A short note on plain convergence of adaptive least-squares finite element methods
论文作者
论文摘要
我们表明，在PDE操作员，网格再填充和标记策略的弱条件下，由规范最小二乘功能驱动的自适应最小二乘有限元方法。与先前的作品相反，我们的简单收敛既不依赖足够细的初始网格，也不依赖于对标记参数的严重限制。最后，我们证明，如果使用合同迭代求解器来获得近似解决方案（例如，使用最佳预处理器的预处理结合梯度方法），收敛仍然有效。结果适用于相当抽象的框架，该框架涵盖了各种模型问题。
We show that adaptive least-squares finite element methods driven by the canonical least-squares functional converge under weak conditions on PDE operator, mesh-refinement, and marking strategy. Contrary to prior works, our plain convergence does neither rely on sufficiently fine initial meshes nor on severe restrictions on marking parameters. Finally, we prove that convergence is still valid if a contractive iterative solver is used to obtain the approximate solutions (e.g., the preconditioned conjugate gradient method with optimal preconditioner). The results apply within a fairly abstract framework which covers a variety of model problems.
