Related papers: A Functionally Connected Element Method for Solvin…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the…
This article presents a novel and comprehensive approach for analyzing bending behavior of the tapered perforated beam under an exponential load. The governing differential equation includes important factors like filling ratio ($\alpha$),…
This article presents a new methodology called deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with TFC. TFC is used to transform PDEs with…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
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…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
We present a projection-based numerical integration technique to deal with embedded interface in finite element (FE) framework. The element cut by an embedded interface is denoted as a cut cell. We recognize elemental matrices of a cut cell…
A Novel Scaled boundary finite element method, initially developed in Civil Engineering, is reformulated for solving boundary value problems in computational electromagnetics.
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…
We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…
In nodal based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney…
In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral…