Related papers: A posteriori and a priori error estimates for line…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
In this paper we study the behavior of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete…
This paper presents an $hp$ a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree $p$ and the wave number $k$. For the discretization, we consider a discontinuous Galerkin formulation that is…
We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consider, instead of the differentiation of the primal problem, a…
A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree…
This paper addresses the local recovery of conservative fluxes and the a posteriori error analysis for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed by means of…
This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary…
We extend the framework of a posteriori error estimation by preconditioning in [Li, Y., Zikatanov, L.: Computers \& Mathematics with Applications. \textbf{91}, 192-201 (2021)] and derive new a posteriori error estimates for H(curl)-elliptic…
This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
We study fully discrete linearized Galerkin finite element approximations to a nonlinear gradient flow, applications of which can be found in many areas. Due to the strong nonlinearity of the equation, existing analyses for implicit schemes…
In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived…
This article introduces a new primal-dual weak Galerkin (PDWG) finite element method for second order elliptic interface problems with ultra-low regularity assumptions on the exact solution and the interface and boundary data. It is proved…
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be…
Standard discontinuous Galerkin methods, based on piecewise polynomials of degree $ \qq=0,1$, are considered for temporal semi-discretization for second order hyperbolic equations. The main goal of this paper is to present a simple and…
We propose a discontinuous Galerkin(DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per…
In this work we present an a posteriori analysis for classes of inconsistent, nonconforming schemes approximating elliptic problems. We show the estimates coincide with existing ones for interior penalty type discontinuous Galerkin…
We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the…