Related papers: Higher-continuity s-version of finite element meth…

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…

The Generalized Finite Element Method (GFEM) is a Partition of Unity Method (PUM), where the trial space of standard Finite Element Method (FEM) is augmented with non-polynomial shape functions with compact support. These shape functions,…

Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…

When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…

In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…

Strain smoothing methods such as the smoothed finite element methods (S-FEMs) and the strain-smoothed element~(SSE) method have successfully improved the performance of finite elements, and there have been numerous applications of them in…

In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…

In the class of immersed boundary (IB) methods, the choice of the delta function plays a crucial role in transferring information between fluid and solid domains. Most prior work has used isotropic kernels that do not preserve the…

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…

Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…

The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…

In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…

We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems.…