Related papers: Generalized mixed and primal hybrid methods with a…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of quasi $\phi$-asymptotically nonexpansive mappings $\{F(S_j)\}_{j=1}^N$, the set of…
Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
Nitsche's method is a well-established approach for weak enforcement of boundary conditions for partial differential equations (PDEs). It has many desirable properties, including the preservation of variational consistency and the fact that…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
This paper proposes a $C^{0}$ (non-Lagrange) primal finite element approximation of the linear elliptic equations in non-divergence form with oblique boundary conditions in planar, curved domains. As an extension of [Calcolo, 58 (2022), No.…
We consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
Hybridizable \(H(\textrm{div})\)-conforming finite elements for symmetric tensors on simplices with barycentric refinement are developed in this work for arbitrary dimensions and any polynomial order. By employing barycentric refinement and…
In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div)-Pk…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
We devise and analyze hybrid polyhedral methods of arbitrary order for the approximation of div-curl systems on three-dimensional domains featuring non-trivial topology. The div-curl systems we are interested in stem from magnetostatics,…
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential…
This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations. The implementation of high order…
We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator…