Related papers: Fuzzy finite element solution of uncertain neutron…
Recently, three successful antineutrino experiments (Daya Bay, Double Chooz, and RENO) measured the neutrino mixing angle theta_{13}; however, significant discrepancies were found, both in the absolute flux and spectral shape. Much effort…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
We consider the diffusive limit of an unsteady neutron transport equation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with…
Nonlocality in the scattering potential leads to an integro-differential equation.In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schroedinger equation is usually handled by…
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
Nuclear Magnetic Resonance (NMR) spectroscopy is a central characterization method for molecular structure elucidation, yet interpreting NMR spectra to deduce molecular structures remains challenging due to the complexity of spectral data…
The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle equation over finite element spaces is constructed and the explicit upper bound of the…
In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
Thermal fission energy is one of the basic parameters needed in the calculation of antineutrino flux for reactor neutrino experiments. It is useful to improve the precision of the thermal fission energy calculation for current and future…
We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…
This dissertation deals with theoretical descriptions of nuclear fission and synthesis of superheavy elements via fusion. The associated shape evolutions are treated using a random-walk approach where both the potential energy and the…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…