相关论文: Parallel hybrid iterative methods for variational …
In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…
For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this paper…
This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the $C^0$ interior penalty, and the WOPSIP schemes. Those methods are modified…
In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and…
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties…
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 introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…
This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…
We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal invariant measure, which may be derived via…
The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…