Related papers: Convergence and optimality of higher-order adaptiv…
Mixed finite element methods with flux errors in $H(div)$-norms and div-least-squares finite element methods require a separate marking strategy in obligatory adaptive mesh-refining. The refinement indicator $\sigma^2(\mathcal…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
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…
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…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
This study presents a novel approach utilizing cluster means to address the non-differentiability issue arising from multiple eigenvalues in eigenfrequency and bandgap optimization. By constructing symmetric functions of repeated…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…
Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…
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…
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lam\'e parameters which are parameterized by a countably infinite number of terms in separate expansions. We estimated the…
This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the…
The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…