Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
Induction heating processes optimization a general optimal control approach
Journal of Computational Physics
Numerical microlocal analysis of harmonic wavefields
Journal of Computational Physics
Finite Elements in Analysis and Design
Feedforward and feedback control of ultrasound surgery
Applied Numerical Mathematics
Plane wave decomposition in the unit disc: convergence estimates and computational aspects
Journal of Computational and Applied Mathematics
Asymptotically derived boundary elements for the Helmholtz equation in high frequencies
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Discontinuous Galerkin methods with plane waves for time-harmonic problems
Journal of Computational Physics
An ultra-weak method for acoustic fluid-solid interaction
Journal of Computational and Applied Mathematics
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
Applied Numerical Mathematics
Feedforward and feedback control of ultrasound surgery
Applied Numerical Mathematics
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers
Journal of Computational and Applied Mathematics
A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates
Journal of Scientific Computing
Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems
Computers and Structures
Journal of Computational Physics
SIAM Journal on Scientific Computing
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version
SIAM Journal on Numerical Analysis
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
SIAM Journal on Numerical Analysis
Challenges in computer applications for ship and floating structure design and analysis
Computer-Aided Design
An ES-FEM for accurate analysis of 3D mid-frequency acoustics using tetrahedron mesh
Computers and Structures
A stable discontinuous Galerkin-type method for solving efficiently Helmholtz problems
Computers and Structures
General DG-Methods for Highly Indefinite Helmholtz Problems
Journal of Scientific Computing
The ultra weak variational formulation of thin clamped plate problems
Journal of Computational Physics
FEM with Trefftz trial functions on polyhedral elements
Journal of Computational and Applied Mathematics
Hi-index | 0.04 |
A new technique to solve elliptic linear PDEs, called ultra weak variational formulation (UWVF) in this paper, is introduced in [B. Després, C. R. Acad. Sci. Paris, 318 (1994), pp. 939--944]. This paper is devoted to an evaluation of the potentialities of this technique. It is applied to a model wave problem, the two-dimensional Helmholtz problem. The new method is presented in three parts following the same style of presentation as the classical one of the finite elements method, even though they are definitely conceptually different methods. The first part is committed to the variational formulation and to the continuous problem. The second part defines the discretization process using a Galerkin procedure. The third part actually studies the efficiency of the technique from the order of convergence point of view. This is achieved using theoretical proofs and a series of numerical experiments. In particular, it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom. An application to scattering problems is presented in a fourth part.