Related papers: Efficient quadrature rules for computing the stiff…
We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double precision…
Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
Locking is a common effect in finite element and isogeometric analysis. In the case of plates, transverse shear locking is most prominent, for shells several other types of locking exist. A common cure are mixed methods that introduce…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…
We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on a traditional leapfrog time integration method and the other based on convolution…
The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
This paper presents a computational framework for modeling wave propagation in geometrically linear elastic materials characterized by algebraically nonlinear constitutive relations. We derive a specific form of the nonlinear wave equation…
Explicit relations of matrices for two-dimensional finite element method with third-order triangular elements are given. They are more simple than relations presented in other works and could be easily implemented in new algorithms for both…
Quadrature rules using higher order digital nets and sequences are known to exploit the smoothness of a function for numerical integration and to achieve an improved rate of convergence as compared to classical digital nets and sequences…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…