相关论文: On the coupling of regularization techniques and t…
This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constraints, specifically those governed by stationary generalized…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
We study the fully explicit numerical approximation of a semilinear elliptic boundary value model problem, which features a monomial reaction and analytic forcing, in a bounded polygon $\Omega\subset\mathbb{R}^2$ with a finite number of…
We consider the isoparametric finite element method (FEM) for the Poisson equation in a smooth domain with the homogeneous Dirichlet boundary condition. Because the boundary is curved, standard triangulated meshes do not exactly fit it.…
This article aims to provide approximate solutions for the non-linear collision-induced breakage equation using two different semi-analytical schemes, i.e., variational iteration method (VIM) and optimized decomposition method (ODM). The…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
In $d$ dimensions, accurately approximating an arbitrary function oscillating with frequency $\lesssim k$ requires $\sim k^d$ degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber $k$ and in $d$…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
We have calculated the $W$-loop contribution to the amplitude of the decay $H \to Z \gamma$ in the unitary gauge through the dispersion method and in the $R_\xi$ gauge using dimensional regularization (DimReg). We show that the results of…
In this paper, we study a time-fractional initial-boundary value problem of Kirchhoff type involving memory term for non-homogeneous materials. The energy argument is applied to derive the a priori bounds on the solution of the considered…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for…
This paper investigates ensemble Kalman inversion (EKI) for variational inverse problems with convex, potentially non-smooth regularization. While deterministic EKI and its Tikhonov-regularized variants have primarily been analyzed for…
In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. {In order to do this}, suitable variational formulations are defined for a nonlinear boundary…