Related papers: An efficient finite element method for computing t…
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…
We introduce a high-order finite element method for approximating the Vlasov-Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge-Kutta schemes for time discretization. To stabilize the…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
In this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface…
The present paper studies finite element discretizations of second-order elliptic boundary value problems with homogeneous right-hand side and inhomogeneous boundary conditions. We establish discrete spatial decay estimates on element…
In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…
We propose and study a scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled nonlinear forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous…
This article focuses on the finite volume method (FVM) as an instrument tool to deal with the non-linear collisional-induced breakage equation (CBE) that arises in the particulate process. Notably, we consider the non-conservative…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…
We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, we present a model problem, describing in detail the features…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…