Related papers: Convergence analysis of numerical schemes for the …
The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom,…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
The aim of this contribution is to address the convergence study of a time and space approximation scheme for an Allen-Cahn problem with constraint and perturbed by a multiplicative noise of It\^o type. The problem is set in a bounded…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
We develop an unfitted compatible finite element discretisation for the Darcy problem based on $H(\mathrm{div})$-conforming flux spaces and discontinuous pressure spaces. The method is designed to preserve pointwise discrete mass…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
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…
In this article, we introduce and study three numerical methods for the Dirichlet Monge Amp\`ere equation in two dimensions. The approaches consist in considering new equivalent problems. The latter are discretized by a wide stencil finite…