Related papers: Asymptotic meshes from $r$-variational adaptation …
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
We construct a one-dimensional first-order theory for functionally graded elastic beams using the variational-asymptotic method. This approach ensures an asymptotically exact one-dimensional equations, allowing for the precise determination…
In this study we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with…
We establish a $\Gamma$-convergence result for $h\to 0$ of a thin nonlinearly elastic 3D-plate of thickness $h>0$ which is assumed to be glued to a support region in the 2D-plane $x_3=0$ over the $h$-2D-neighborhood of a given closed set…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain $\Omega$ and its complement, where the exterior problem is restated by an integral equation…
We consider a family of three-dimensional stiffened plates whose dimensions are scaled through different powers of a small parameter $\varepsilon$. The plate and the stiffener are assumed to be linearly elastic, isotropic, and homogeneous.…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider…
In this paper, we establish the asymptotic expressions for the gradient of a solution to the Lam\'{e} systems with partially infinity coefficients as two rigid $C^{1,\gamma}$-inclusions are very close but not touching. The novelty of these…
We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$.…
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…
We obtain a compactness result for $\Gamma$-convergence of integral functionals defined on $\mathcal{A}$-free vector fields. This is used to study homogenization problems for these functionals without periodicity assumptions. More…
We consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet, and identify the $\Gamma$-limit as the sheet thickness goes to 0, thus extending the previous work of the first author [Bella,…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…