论文标题
非对称线性椭圆pdes的自适应fem，准最佳总体成本
Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs
论文作者
论文摘要
我们考虑了在松弛仪引理框架中的一般非对称二阶线性椭圆PDE。我们以任意多项式程度来制定和分析一种自适应有限元算法，该算法引导自适应网状网络再填充和出现的线性系统的不精确迭代溶液。更准确地说，迭代求解器作为外环采用所谓的Zarantonello迭代来对称系统，并作为内部循环，是一种均匀的承包代数求解器，例如，最佳预先预处理的共轭梯度方法或最佳的最佳几何多机元素多机多族多族多机元素。我们证明，所提出的不精确的自适应迭代式对称性有限元法（AISFEM）会导致完整的线性收敛，并且对于足够小的适应性参数，可以相对于整体计算成本，即总计算时间。数值实验强调了理论。
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive mesh-refinement and the inexact iterative solution of the arising linear systems. More precisely, the iterative solver employs, as an outer loop, the so-called Zarantonello iteration to symmetrize the system and, as an inner loop, a uniformly contractive algebraic solver, e.g., an optimally preconditioned conjugate gradient method or an optimal geometric multigrid algorithm. We prove that the proposed inexact adaptive iteratively symmetrized finite element method (AISFEM) leads to full linear convergence and, for sufficiently small adaptivity parameters, to optimal convergence rates with respect to the overall computational cost, i.e., the total computational time. Numerical experiments underline the theory.
