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In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact…
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…
Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate…
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…
We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
We introduce Prior-Informed Flow Matching (PIFM), a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while…
Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…
We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change, using a one-fluid approach. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with…
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite…
We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
The present work is devoted to approximation of the statistical moments of the unknown solution of a class of elliptic transmission problems in $\mathbb R^3$ with randomly perturbed interfaces. Within this model, the diffusion coefficient…
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing…