A minimum Sobolev norm technique for the numerical discretization of PDEs

Abstract

Partial differential equations (PDEs) are discretized into an under-determined system of equations and a minimum Sobolev norm solution is shown to be efficient to compute and converge under very generic conditions. Numerical results of a single code, that can handle PDEs in first-order form on complicated polygonal geometries, are shown for a variety of PDEs: variable coefficient div–curl, scalar elliptic PDEs, elasticity equation, stationary linearized Navier–Stokes, scalar fourth-order elliptic PDEs, telegrapher's equations, singular PDEs, etc.