# Calcolo

## List of Papers (Total 15)

#### Revisiting generalized FEM: a Petrov–Galerkin enrichment based FEM interpolation for Helmholtz problem

A concept of Petrov–Galerkin enrichment which is appropriate for highly accurate and stable interpolation of variational solutions is introduced. In the finite element context, the setting refers to standard trial functions for the solution, while the test space will be enriched. The FEM interpolation procedure that we propose will be justified by local wavelets with vanishing...

#### Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and...

#### A posteriori error analysis of a fully-mixed formulation for the Brinkman–Darcy problem

We develop the a posteriori error analysis for a mixed finite element method applied to the coupling of Brinkman and Darcy equations in 3D, modelling the interaction of viscous and non-viscous flow effects across a given interface. The system is formulated in terms of velocity and pressure within the Darcy subdomain, together with vorticity, velocity and pressure of the fluid in...

#### Iterative method for solving nonlinear singular problems

The aim of our work is to present a method (p-factor method) for solving nonlinear equations of the form \begin{aligned} F(x)=0, \quad F:\mathbb {R}^n\rightarrow \mathbb {R}^m, \end{aligned}in singular (irregular) case, i.e. when the matrix $$F'(x)$$ is singular at an initial point $$x_0$$ of an iterative sequence $$\{x_k\}$$, $$k=1,2,\ldots$$ We investigate conditions that...

#### Method of lines for parabolic functional differential equations on cylindrical domains

The numerical method of lines is a technique for solving partial differential equations by discretising in all but one dimension. In this paper the solution of the approximate problem is extended outside the domain using the boundary condition. This leads to functional differential-algebraic equations. Sufficient conditions for the well-posedness, stability and convergence of the...

#### Duality for multiobjective variational control problems with $$(\Phi , \rho )$$ -invexity

In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under $$(\Phi , \rho )$$-invexity. The results generalize a number of duality results previously established for multiobjective...

#### On the numerical approximation of viscosity solutions for the differential-functional Cauchy problem

We consider the Cauchy problem for first order differential-functional equations. We present finite difference schemes to approximate viscosity solutions of this problem. The functional dependence in the equation is of the Hale type. It contains, as a particular case, equation with a retarded and deviated argument, and differential-integral equation. Numerical examples to...

#### Bubble stabilized discontinuous Galerkin methods on conforming and non-conforming meshes

The aim of this paper is to discuss the properties of the bubble stabilized discontinuous Galerkin method with respect to mesh geometry. First we show that on certain non-conforming meshes the bubble stabilized discontinuous Galerkin method allows for hanging nodes/edges. Then we consider the case of conforming meshes and present a post-processing algorithm based on the Crouzeix...

#### Computational issues related to iterative coupling of subsurface and channel flows

Abstract We consider solution techniques for the coupling of Darcy and Stokes flow problems. The study was motivated by the simulation of the interaction between channel flow and subsurface water flow for realistic data and arbitrary interfaces between the two different flow regimes. Here, the emphasis is on the efficient iterative solution of the coupled problem based on...

#### A discrete de Rham complex with enhanced smoothness

Discrete de Rham complexes are fundamental tools in the construction of stable elements for some finite element methods. The purpose of this paper is to discuss a new discrete de Rham complex in three space dimensions, where the finite element spaces have extra smoothness compared to the standard requirements. The motivation for this construction is to produce discretizations...