Related papers: Space-time finite element methods for the initial …
We consider the approximation to the solution of the initial boundary value problem for the heat equation with right hand side and initial condition that merely belong to $L^1$. Due to the low integrability of the data, to guarantee…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study [16] attempted to reconstruct the unknown…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
A fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) and 2 + 1 dimensions to explore critical collapse and search for self-similar solutions.…
We consider finite volume (or equivalently, finite temperature) expectation values of local operators in integrable quantum field theories using a combination of numerical and analytical approaches. It is shown that the truncated conformal…
We propose a new analysis of convergence for a $k$th order ($k\ge 1$) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
This paper presents a modified quasi-reversibility method for computing the exponentially unstable solution of a nonlocal terminal-boundary value parabolic problem with noisy data. Based on data measurements, we perturb the problem by the…
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a…
We solve an inverse problem for the one-dimensional heat diffusion equation. We reconstruct the heat source function for the three types of data: 1) single position point and different times, 2) constant time and uniformly distributed…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and 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…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins--Sekerka problem. The discretization uses…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…