Related papers: Fine error bounds for approximate asymmetric saddl…
This paper directly builds upon previous work where we introduced new reduced basis a posteriori error bounds for parametrized saddle point problems based on Brezzi's theory. We here sharpen these estimates for the special case of a…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
We analyze a finite element/boundary element procedure to solve a non-convex contact problem for the double-well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain…
This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: $\min_x\max_yf(x,y)$. Under the standard first-order smoothness conditions where $f$ is…
We investigate saddlepoint approximations applied to the score test statistic in genome-wide association studies with binary phenotypes. The inaccuracy in the normal approximation of the score test statistic increases with increasing sample…
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…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…
All finite element methods, as well as much of the Hilbert-space theory for partial differential equations, rely on variational formulations, that is, problems of the type: find $u\in V$ such that $a(v,u) = l(v)$ for each $v\in L$, where…
The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study…
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate derivatives of functions from values at scattered nodes…
This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for which a "good" macroscopic description in the form of…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…