相关论文: An a posteriori verification method for generalize…
Eigenvalue analysis based methods are well suited for the reconstruction of finitely supported measures from their moments up to a certain degree. We give a precise description when Prony's method succeeds in terms of an interpolation…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and…
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…
In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities…
One of the requirements imposed on the realistic quantum computers is to provide computation results which can be repeated and reproduced. In the situation when one needs to repeat the quantum computation procedure several times, it is…
Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…
This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-structure additive Runge--Kutta (GARK) approach to time…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local…
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The…
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality…
In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…
We develop an \textit{a posteriori} error analysis for a numerical estimate of the time at which a functional of the solution to a partial differential equation (PDE) first achieves a threshold value on a given time interval. This quantity…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…