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We consider the isoparametric finite element method (FEM) for the Poisson equation in a smooth domain with the homogeneous Dirichlet boundary condition. Because the boundary is curved, standard triangulated meshes do not exactly fit it.…
In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM…
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…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories…
In this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty, here proposed, is that curved elements are naturally handled without any degradation of the solution accuracy. In…
We study the problem of computing the exterior modulus of a bounded quadrilateral. We reduce this problem to the numerical solution of the Dirichlet-Neumann problem for the Laplace equation. Several experimental results, with error…
Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE…
This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder.…
In this paper we analyze a class of trace finite element methods (TraceFEM) for the discretization of vector-Laplace equations. A key issue in the finite element discretization of such problems is the treatment of the constraint that the…
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 present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
In this paper, we employ the techniques developed for second order operators to obtain the new estimates of Virtual Element Method for fourth order operators. The analysis is based on elements with proper shape regularity. Estimates for…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
In this work is provided a numerical study of a diffusion problem involving a second order term on the domain boundary (the Laplace-Beltrami operator) referred to as the \textit{Ventcel problem}.A variational formulation of the Ventcel…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
Many applications like subseismic fault modeling, fractured reservoir modeling and interpretation/validation of fault connectivity involve the solution to an elliptic boundary value problem in a background medium perturbed by the presence…
The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second order in time method for curve diffusion. Both schemes are…