论文标题
完全非线性椭圆方程的最小二乘Galerkin梯度恢复方法
A least-squares Galerkin gradient recovery method for fully nonlinear elliptic equations
论文作者
论文摘要
我们提出了基于galerkin的最小二乘梯度恢复，以近似dirichlet问题，以解决非散发形式的线性椭圆形问题，以及相应的apriori和aposteriori误差界。这种方法用于解决完全非线性椭圆问题，例如Monge-Ampère，Hamilton-Jacobi-Bellman，使用光滑（香草）和半齿牛顿线性化。我们讨论了数值结果，包括基于Aposteriori误差指标的自适应方法。
We propose a least squares Galerkin based gradient recovery to approximate Dirichlet problems for strong solutions of linear elliptic problems in nondivergence form and corresponding apriori and aposteriori error bounds. This approach is used to tackle fully nonlinear elliptic problems, e.g., Monge-Ampère, Hamilton-Jacobi-Bellman, using the smooth (vanilla) and the semismooth Newton linearization. We discuss numerical results, including adaptive methods based on the aposteriori error indicators.
