Related papers: Multiscale Finite Element approach for "weakly" ra…
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…
We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…
We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear…
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coefficients. Building upon the work of Kaarnioja, Kazashi, Kuo,…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…