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We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution $u \in H^s$…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
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…
For a singularly perturbed elliptic model problem with two small parameters, we analyze finite element methods of any order on a Bakhvalov-type mesh. For convergence analysis, we construct a new interpolation by using the characteristics of…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
We reconsider the ellipsoid method for linear inequalities. Using the ellipsoid representation of Burrell and Todd, we show the method can be viewed as coordinate descent on the volume of an enclosing ellipsoid, or on a potential function,…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
The paper deals with two nonlinear elliptic equations with $(p,q)$-Laplacian and the Dirichlet-Neumann-Dirichlet (DND) boundary conditions, and Dirich\-let-Neu\-mann-Neumann (DNN) boundary conditions, respectively. Under mild hypotheses, we…
In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which…
A boundary value problem for a fractional power $0 < \varepsilon < 1$ of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when $\varepsilon \rightarrow 0$. It is solved numerically using a…
We will study a free boundary value problem driven by a source term which is quite {\it irregular}. In the process, we will establish a monotonicity result, and regularity of the solution.
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
An $hp$ version of interface penalty finite element method ($hp$-IPFEM) is proposed for elliptic interface problems in two and three dimensions on unfitted meshes. Error estimates in broken $H^1$ norm, which are optimal with respect to $h$…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…