Which designers need nonlinear FEA and why? Actually, projects ranging from designing a paper clip to a high-rise can benefit from the technique. A linear FEA study somewhat simulates reality only ...

This result then opens a door for constructing convergent finite element methods for the fully nonlinear second-order equations, a task which has been impracticable before. The goal of this paper is ...

This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Thanks to these abilities, they can already topple complex linear differential equations exponentially faster than classical machines. Researchers have long hoped they could similarly tame nonlinear ...