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Nonconforming finite element Stokes complexes in three dimensions
Two nonconforming finite element Stokes complexes starting from the conforming Lagrange element and ending with the nonconforming P 1 - P 0 element for...
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Conforming and Nonconforming Virtual Element Methods for Signorini Problems
In this paper, we design and analyze the conforming and nonconforming virtual element methods for the Signorini problem. Under some regularity...
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The Nonconforming Virtual Element Method with Curved Edges
We introduce a nonconforming virtual element method for the Poisson problem on domains with fixed curved boundary and internal interfaces. We prove...
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Least-Squares Methods with Nonconforming Finite Elements for General Second-Order Elliptic Equations
In this paper, we study least-squares finite element methods (LSFEM) for general second-order elliptic equations with nonconforming finite element...
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Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions
In this article we present the nonconforming spectral element method (NSEM) for linear second-order ordinary differential equations with boundary...
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The nonconforming virtual element method for optimal control problem governed by Stokes equations
In this paper we investigate the lowest-order nonconforming virtual element approximation of optimal control problem governed by Stokes equations....
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Fast and Accuracy-Preserving Domain Decomposition Methods for Reduced Fracture Models with Nonconforming Time Grids
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway...
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Unconditional superconvergence analysis of an energy dissipation property preserving nonconforming FEM for nonlinear BBMB equation
In this article, an energy dissipation property preserving modified Crank–Nicolson (CN) fully-discrete scheme is developed and investigated with the...
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Nonconforming Finite Element Methods of Order Two and Order Three for the Stokes Flow in Three Dimensions
In this study, the nonconforming finite elements of order two and order three are constructed and exploited for the Stokes problem. The moments of...
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The Stabilized Nonconforming Virtual Element Method for Linear Elasticity Problem
We present the stabilized nonconforming virtual element method for linear elasticity problem in two dimensions. The jump penalty term is introduced...
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A Domain Decomposition Method for Nonconforming Finite Element Approximations of Eigenvalue Problems
Since the nonconforming finite elements (NFEs) play a significant role in approximating PDE eigenvalues from below, this paper develops a new and...
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Performance of nonconforming spectral element method for Stokes problems
A nonconforming spectral element method for the Stokes problem on nonsmooth domains has been proposed in Mohapatra et al. (J Comput Appl Math...
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Cut-Off Error Splitting Technique for Conservative Nonconforming VEM for N-Coupled Nonlinear Schrödinger–Boussinesq Equations
In this work, the error splitting technique combined with cut-off function method is designed to derive unconditionally optimal error estimates for a...
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Convergence and Superconvergence Analysis of a Nonconforming Finite Element Variable-Time-Step BDF2 Implicit Scheme for Linear Reaction-Diffusion Equations
In this paper, an effective fully-discrete implicit scheme for solving linear reaction-diffusion equations is constructed by using the...
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High accuracy analysis of a nonconforming rectangular finite element method for the Brinkman model
We propose a simple nonconforming rectangular finite element method for the Brinkman model. The velocity space is edge-oriented, in which the local...
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Iterative Methods with Nonconforming Time Grids for Nonlinear Flow Problems in Porous Media
Partially saturated flow in a porous medium is typically modeled by the Richards equation, which is nonlinear, parabolic and possibly degenerated....
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A Nonconforming Virtual Element Method for a Fourth-order Hemivariational Inequality in Kirchhoff Plate Problem
This paper is devoted to a fourth-order hemivariational inequality for a Kirchhoff plate problem. A solution existence and uniqueness result is...
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An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations
This paper presents a nonconforming finite element scheme for the planar biharmonic equation, which applies piecewise cubic polynomials ( P 3 ) and...
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The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. As for the latter, we show a new...
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Superconvergent Flux Recovery of the Rannacher–Turek Nonconforming Element
This work presents superconvergence estimates of the nonconforming Rannacher–Turek element for second order elliptic equations on any cubical meshes...