Superconvergence

Superconvergence is a phenomenon observed in numerical analysis and computational mathematics, particularly in the context of finite element methods, finite difference methods, and other numerical discretization techniques used for solving partial differential equations (PDEs). It refers to a situation where the convergence rate of a numerical approximation to the exact solution exceeds the expected rate based on the mathematical theory of convergence. In typical scenarios, one would expect that the convergence of a numerical solution would improve as the mesh or time step is refined.