numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

, a superconvergent or supraconvergent method is one which converges faster than generally expected (''superconvergence'' or ''supraconvergence''). For example, in the

Finite Element Method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

approximation to

Poisson's equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with th ...

in two dimensions, using piecewise linear elements, the average error in the

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...

is first order. However under certain conditions it's possible to recover the gradient at certain locations within each element to second order.

References

* * * Finite element method Numerical analysis {{mathapplied-stub