8 citations · 24 across the 11 of their papers we have counts for
11 papers
Optimal enforcement of natural conditions on smooth boundaries with piecewise polynomials upon fitted straight-edged meshes
Vitoriano Ruas
A few decades ago some possible remedies to an inaccurate enforcement of Neumann or Robin conditions prescribed on the boundary of a smooth domain, owing to its approximation by th…
A variant of the Raviart-Thomas method to handle smooth domains using straight-edged triangles. Part II -- Approximation results
Fleurianne Bertrand, Vitoriano Ruas
In arXiv:2307.03503 [math.NA] we commenced to study a variant of the Raviart-Thomas mixed finite element method for triangles, to solve second order elliptic equations in a curved…
Fine error bounds for approximate asymmetric saddle point problems
Vitoriano Ruas
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades…
A variant of the Raviart-Thomas method for smooth domains with straight-edged triangles
Fleurianne Bertrand, Vitoriano Ruas
Several physical problems modeled by second-order elliptic equations can be efficiently solved using mixed finite elements of the Raviart-Thomas family RTk for N-simplexes, introdu…
Optimal-rate Lagrange and Hermite finite elements for Dirichlet problems in curved domains with straight-edged triangles
Vitoriano Ruas
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved…
Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary
L. Beilina, V. Ruas
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, us…
An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood
Larisa Beilina, Vitoriano Ruas
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard…
Methods of arbitrary optimal order with tetrahedral finite-element meshes forming polyhedral approximations of curved domains
Vitoriano Ruas
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order bounda…
One-parameter tetrahedral mesh generation for spheroids
Vitoriano Ruas
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Bes…
Optimal simplex finite-element approximations of arbitrary order in curved domains circumventing the isoparametric technique
Vitoriano Ruas
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reas…
Hermite finite elements for convection-diffusion equations
Florin Radu, Vitoriano Ruas, Paulo Trales
This work addresses techniques to solve convection-diffusion problems based on Hermite interpolation. We extend to the case of these equations a Hermite finite element method provi…