About: Hp-FEM

hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of variable size(h) and polynomial degree (p). The origins of hp-FEM date back to the pioneering work of Barna A. Szabó and Ivo Babuška who discovered that the finite element method converges exponentially fast whenthe mesh is refined using a suitable combination of h-refinements(dividing elements into smaller ones) and p-refinements (increasing theirpolynomial degree). The exponential convergence makes the method very attractive compared to most other finite element methods, which only converge with an algebraic rate. The exponential convergenceof hp-FEM was not only predicted theoretically, but als