New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

SIAM Journal on Numerical Analysis, Vol. 55, No. 1 (2017), pp. 63-86 (24 pages) A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and ...

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and ...