Related papers: Energy-stable parametric finite element approximat…
We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom…
We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between…
This paper deals with the numerical study of a strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. Furthermore, the recently proposed Asymptotic-Preserving…
An evolution partial differential equation for the surface of a non-wetting single-crystal film in an attractive substrate potential is derived and used to study the dynamics of a pinhole for the varying initial depth of a pinhole and the…
We develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neighborhood of a point at the boundary. Our…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
The purpose of this study is threefold: first, to identify a scheme for the determination of the surface energy coefficient a_surf that offers the best compromise between robustness, precision, and numerical efficiency; second, to analyze…