Adaptive FEM with quasi-optimal overall cost for nonsymmetric linear elliptic PDEs

We consider a general nonsymmetric second-order linear elliptic PDE in the framework of Lax-Milgram lemma. formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers mesh-refinement inexact iterative solution arising systems. More precisely, solver employs, as outer loop, so-called Zarantonello iteration to symmetrize system and, inner uniformly contractive algebraic solver, e.g., optimally preconditioned conjugate gradient method or optimal geometric multigrid algorithm. prove proposed iteratively symmetrized (AISFEM) leads full convergence for sufficiently small adaptivity parameters, rates respect overall computational cost, i.e., total time. Numerical experiments underline theory.