论文标题
在双重不连续的galerkin Norm中，以目标为导向的适应性
Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm
论文作者
论文摘要
我们提出了一种面向目标的网状自适应算法，以通过在双重不连续的 - 盖尔金规范上进行残留最小化稳定的有限元方法。通过解决鞍点问题，这种残留最小化可以在每个网格实例上与溶液的连续近似以及对损坏的多项式空间的残留投影，这是一个可靠的误差估计器，可通过自动网格改进来最大程度地减少离散能量标准。在这项工作中，我们提出和分析了一种稳定的残留最小化的面向目标的自适应算法。考虑到相同的鞍点配方和不同的右侧，我们解决了原始问题和伴随问题。通过解决第三个稳定问题，我们获得了两个有效的错误估计，以指导面向目标的适应性。我们说明了这种面向目标的自适应策略在对流扩散反应问题上的表现。
We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable continuous approximation to the solution on each mesh instance and a residual projection onto a broken polynomial space, which is a robust error estimator to minimize the discrete energy norm via automatic mesh refinement. In this work, we propose and analyze a goal-oriented adaptive algorithm for this stable residual minimization. We solve the primal and adjoint problems considering the same saddle-point formulation and different right-hand sides. By solving a third stable problem, we obtain two efficient error estimates to guide goal-oriented adaptivity. We illustrate the performance of this goal-oriented adaptive strategy on advection-diffusion-reaction problems.
