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This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via ...
We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, ...
We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and polyhedral meshes. The mimetic inner products are locally ...
A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure-driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow ...
We study a class of models at the interface between statistics and numerical analysis. Specifically, we consider nonparametric regression models for the estimation of spatial fields from pointwise and noisy observations, which account for problem-specific ...
Numerical analysis of linear visco-elastic materials requires robust and stable methods to integrate partial differential equations in both space and time. In this paper, symmetric space-time finite element operators are derived for the first time for elem ...
The goal of this project is to numerically solve the Navier-Stokes equations by using different numerical methods with particular emphasis on solving the problem of the flow past a square cylinder. In particular, we use the finite element method based on P ...
An anisotropic a posteriori error estimate is derived for a finite element discretization of the wave equation in two space dimensions. Only the error due to space discretization is considered, and the error estimates are derived in the nonnatural L-2(0, T ...
A finite element heterogeneous multiscale method is proposed for the wave equation with highly oscillatory coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coeff ...
Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the lin ...