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Article
Open AccessWhen rational functions meet virtual elements: the lightning virtual element method
We propose a lightning Virtual Element Method that eliminates the stabilisation term by actually computing the virtual component of the local VEM basis functions using a lightning approximation. In particular,...
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Article
Open AccessA block quaternion GMRES method and its convergence analysis
We consider the quaternion linear system \(AX = B\) A X ...
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Article
Open AccessAnalytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon
In an open, bounded Lipschitz polygon \(\Omega \subset \mathbb {R}^2\) Ω ...
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Article
Open AccessHigh-order schemes based on extrapolation for semilinear fractional differential equation
By rewriting the Riemann–Liouville fractional derivative as Hadamard finite-part integral and with the help of piecewise quadratic interpolation polynomial approximations, a numerical scheme is developed for a...
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Article
Open AccessRobust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms
This article deals with two different numerical approaches for solving singularly perturbed parabolic problems with time delay and interior layers. In both approaches, the implicit Euler scheme is used for the...
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Article
Open AccessA linear algebra perspective on the random multi-block ADMM: the QP case
Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct multi-block generali...
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Article
Open AccessPreconditioning of discrete state- and control-constrained optimal control convection-diffusion problems
We consider the iterative solution of algebraic systems, arising in optimal control problems constrained by a partial differential equation with additional box constraints on the state and the control variable...
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Article
Open AccessLocal projection stabilized finite element methods for advection–reaction problems
An a priori analysis for generalized local projection stabilized finite element approximations for the solution of an advection–reaction equation is presented in this article. The stability and a priori error est...
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Article
Open AccessThe Fréchet derivative of the tensor t-function
The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer Linear Algebra Appl 27(3):e2288). In this work, we investigate p...
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Open AccessCohomology of the discrete de Rham complex on domains of general topology
In this work we prove that, for a general polyhedral domain of \(\mathbb {R}^3\) ...
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Open AccessCorrection: Mesh quality agglomeration algorithm for the virtual element method applied to discrete fracture networks
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Open AccessMesh quality agglomeration algorithm for the virtual element method applied to discrete fracture networks
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated with a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The p...
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Open AccessIterative optimal solutions of linear matrix equations for hyperspectral and multispectral image fusing
For a linear matrix function f in \(X \in {\mathbb {R}}^{m\times n}\) X ...
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Open AccessOn the convergence of numerical integration as a finite matrix approximation to multiplication operator
We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, converg...
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Article
Open AccessThe infinite Lanczos method for symmetric nonlinear eigenvalue problems
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then ...
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Article
Open AccessNew error estimates of Lagrange–Galerkin methods for the advection equation
We study in this paper new developments of the Lagrange–Galerkin method for the advection equation. In the first part of the article we present a new improved error estimate of the conventional Lagrange–Galerk...
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Article
Open AccessTowards nonuniform distributions of unisolvent weights for high-order Whitney edge elements
We propose to extend results on the interpolation theory for scalar functions to the case of differential k-forms. More precisely, we consider the interpolation of fields in
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Open AccessA semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positiv...
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Open AccessNumerical approximation and simulation of the stochastic wave equation on the sphere
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to d...
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Article
Open AccessHigh-order interpolatory Serendipity Virtual Element Method for semilinear parabolic problems
We present an efficient method for the numerical approximation of a general class of two dimensional semilinear parabolic problems on polygonal meshes. The proposed approach takes advantage of the properties o...
