相关论文: On optimal finite element schemes for biharmonic e…

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

In this work, a polygonal Reissner-Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced…

In this paper, we rigorously study an order 2 scheme that was previously proposed by some of the authors. A slight modification is proposed that enables us to prove the convergence of the scheme while simplifying in the same time the inner…

We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator.…

A piecewise continuous biharmonic problem in domains with corner points and a corresponding Schwarz type boundary value problem for monogenic functions in a commutative biharmonic algebra are considered. A method for reducing the problems…

Finite element exterior calculus (FEEC) has been developed as a systematical framework for constructing and analyzing stable and accurate numerical method for partial differential equations by employing differential complexes. This paper is…

Stencil composition uses the idea of function composition, wherein two stencils with arbitrary orders of derivative are composed to obtain a stencil with a derivative order equal to sum of the orders of the composing stencils. In this…

Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient…

A unified construction of canonical $H^m$-nonconforming finite elements is developed for $n$-dimensional simplices for any $m, n \geq 1$. Consistency with the Morley-Wang-Xu elements [Math. Comp. 82 (2013), pp. 25-43] is maintained when $m…

This paper presents a novel stabilized nonconforming finite element method for solving the surface biharmonic problem. The method extends the New-Zienkiewicz-type (NZT) element to polyhedral (approximated) surfaces by employing the Piola…

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly-imposed Dirichlet boundary conditions using polynomial B-splines.

We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…

We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…

We present and analyse a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we…

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…

This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…

In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite…

We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…