A mixed method for 4th order problems using linear finite elements
A mixed–FEM and BEM coupling for a three-dimensional eddy current problem
We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
A mixed–FEM and BEM coupling for a three-dimensional eddy current problem
We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the...
A mixed-Lagrange multiplier finite element method for the polyharmonic equation
A modal synthesis method for the elastoacoustic vibration problem
A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved, error...
A modal synthesis method for the elastoacoustic vibration problem
A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with Lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved,...
A modification of the two-level algorithm with overcorrection
In this paper we analyse an algorithm which is a modification of the so-called two-level algorithm with overcorrection, published in [2]. We illustrate the efficiency of this algorithm by a model example.
A modified quasi-boundary value method for the backward time-fractional diffusion problem
In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an a priori regularization parameter...
A moving mesh fictitious domain approach for shape optimization problems
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
A multigrid algorithm for higher order finite elements on sparse grids.
A Multi-Grid Algorithm for Mixed Problems with Penalty.
A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.
A multigrid method for Reissner-Mindlin plates.
A multigrid method for saddle point problems arising from mortar finite element discretizations.
A multilevel adaptive mesh generation scheme using Kd-trees.
A Multilevel Algorithm for the Biharmonic Problem.
A multilevel method with correction by aggregation for solving discrete elliptic problems
The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.