Related papers: Stability estimate for the discrete Calderon probl…

This paper concerns the numerical solution of three-dimensional degenerate Kawarada equations. These partial differential equations possess highly nonlinear source terms, and exhibit strong quenching singularities which pose severe…

We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…

We consider the problem of the continuation with respect to a small parameter $\epsilon$ of spatially localised and time periodic solutions in 1-dimensional dNLS lattices, where $\epsilon$ represents the strength of the interaction among…

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…

We study the Dirichlet problem for discrete harmonic functions in unbounded product domains on multidimensional lattices. First we prove some versions of the Phragm\'en-Lindel\"of theorem and use Fourier series to obtain a discrete analog…

In this work we consider a discontinuous Galerkin method for the discretization of the Stokes problem. We use $H(\textrm{div})$-conforming finite elements as they provide major benefits such as exact mass conservation and…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and…

Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…

In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition…

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

We prove a global logarithmic stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional domain.

In this article, we give a unified theory for constructing boundary layer expansions for dis-cretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the…

We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…

In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…

The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…

The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…

We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded…

The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…

We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…