Related papers: Discrete least-squares finite element methods
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
A finite element discretization is developed for the Cai-Hu model, describing the formation of biological networks. The model consists of a non linear elliptic equation for the pressure $p$ and a non linear reaction-diffusion equation for…
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…
A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
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…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…
This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…
The very weak solution of the Poisson equation with $L^2$ boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the $L^2(\Omega)$-norm with order $1/2$ in convex…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…