This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Given an arbitrary function in, we show that the error attained by the global-best
approximation by-conforming piecewise polynomial Raviart–Thomas–Nédélec elements …

In this work we design and analyse a Discrete de Rham (DDR) method for the
incompressible Navier–Stokes equations. Our focus is, more specifically, on the SDDR …

For the Hodge–Laplace equation in finite element exterior calculus, we introduce several
families of discontinuous Galerkin methods in the extended Galerkin framework. For …

We study the numerical approximation of sign-shifting problems of elliptic type. We fully
analyze and assess the method briefly introduced in [A. Abdulle, ME Huber and S. Lemaire …

We present an abstract framework for the eigenvalue approximation of a class of non-
coercive operators. We provide sufficient conditions to guarantee the spectral correctness of …

We present an efficient numerical method to approximate the flux variable for the Darcy flow
model. An important feature of our new method is that the approximate solution for the flux …

We address fundamental aspects in the approximation theory of vector-valued finite element
methods, using finite element exterior calculus as a unifying framework. We generalize the …

We develop commuting finite element projections over smooth Riemannian manifolds. This
extension of finite element exterior calculus establishes the stability and convergence of …