Related papers: A Tikhonov approach to level set curvature computa…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…
A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors.…
The handling of topology changes in two-phase flows, such as breakup or coalescence of interfaces, with front tracking is a well-known problem that requires an additional effort to perform explicit manipulations of the Lagrangian front. In…
We propose in this paper a discretization of the momentum convection operator for fluid flow simulations on quadrangular or hexahedral meshes. The space discretization is performed by the loworder nonconforming Rannacher-Turek finite…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
A finite element method of any order is applied on a Bakhvalov-type mesh to solve a singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential boundary layers. A uniform convergence of (almost) optimal…
It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
In this paper, we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that…
We introduce a novel algorithm that converges to level-set convex viscosity solutions of high-dimensional Hamilton-Jacobi equations. The algorithm is applicable to a broad class of curvature motion PDEs, as well as a recently developed…
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…
Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…
Using tools from the theory of operator ideals and s-numbers, we develop a general approach to transfer estimates for $L_2$ -approximation of Sobolev functions into estimates for $L_\infty$-approximation, with precise control of all…
Regularizing a linear ill-posed operator equation can be achieved by manipulating the spectrum of the operator's pseudo-inverse. Tikhonov regularization and spectral cutoff are well-known techniques within this category. This paper…
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…
This paper discusses a relation between the re-initialization equation of the level-set functions derived by Wac{\l}awczyk [J.Comp.Phys., 299, (2015)] and the condition for the phase equilibrium provided by the stationary solution to the…