Related papers: A Posteriori Error Estimator for a Front-Fixing Fi…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques…
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved…
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed by solving global optimization problems, which could be…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
In our work, we consider the classical density-based approach to the topology optimization. We propose to modify the discretized cost functional using a posteriori error estimator for the finite element method. It can be regarded as a new…
We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not…
A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable…
A residual based {\em a posteriori} error estimator is derived for a quadratic finite element method (fem) for the elliptic obstacle problem. The error estimator involves various residuals consisting the data of the problem, discrete…
In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…