Papers by Rodolfo Bermejo
Sema Journal Boletin De La Sociedad Espanola De Matematica Aplicada, 2008
We propose in this paper a space-time adaptive algorithm based on the Dual Weighted Residual (DWR... more We propose in this paper a space-time adaptive algorithm based on the Dual Weighted Residual (DWR) idea in the framework of finite element method. Our algorithm consists of applying the DWR technique locally in each time interval I_n := (t_{n−1}, t_n], thus, we control the local or truncation error for a functional of the solution J(u). That means that we can define a self-sufficient criterium that allows us to have control of the time step Delta t and the mesh size h as time progresses. Another good feature of our algorithm is the extension of the spatial post-processing procedure of the traditional DWR method to unstructured meshed made of simplices. Key words: Finite elements, semi-Lagrangian method, a posteriori error estimator, Dual Weighted Residual method, unstructured triangular meshes. AMS subject classifications: 65N30 65M60
We present in this paper a numerical study of long-term calculations of an idealized mid-latitude... more We present in this paper a numerical study of long-term calculations of an idealized mid-latitude ocean circulation model. The objective of this paper is twofold. First, we present an efficient semi-Lagrangia scheme for eddy resolving ocean circulation models, and second, we use the so called proper orthogonal decomposition technique to characterize the finite dimensional manifold that contains the attractor of the solution. Using a Galerkin projection on this manifold we reduce the high dimensional system obtained by the application of the finite element method, to a low-dimensional one and , thus, we can calculate the bifurcation diagram with the horizontal eddy viscosity coefficient as a control parameter. Introduction On the large scale, the ocean circulation system is driven by wind-stress, heat and fresh water fluxes. The wind-stress is the main driving mechanism of the surface circulation, whereas heat and fresh water fluxes are responsible of the thermohaline circulation, wh...
SIAM Journal on Numerical Analysis, 1995
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Siam Journal on Numerical Analysis, Nov 29, 2012
ABSTRACT We introduce a second order in time modified Lagrange-Galerkin (MLG) method for the time... more ABSTRACT We introduce a second order in time modified Lagrange-Galerkin (MLG) method for the time dependent incompressible Navier-Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the P2/P1 Taylor-Hood element are used.
Monthly Weather Review, Nov 1, 1992
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Xxiii Congreso De Ecuaciones Diferenciales Y Aplicaciones Xiii Congreso De Matematica Aplicada Xxiii Congreso De Ecuaciones Diferenciales Y Aplicaciones Xiii Congreso De Matematica Aplicada 9 13 Septiembre 2013 Castellon, 2013
Siam Journal on Scientific Computing, May 21, 2000
A Multigrid Algorithm for the p-Laplacian. [SIAM Journal on Scientific Computing 21, 1774 (2000)]... more A Multigrid Algorithm for the p-Laplacian. [SIAM Journal on Scientific Computing 21, 1774 (2000)]. Rodolfo Bermejo, Juan-Antonio Infante. Abstract. We introduce a full approximation storage (FAS) multigrid algorithm to find the ...
Page 1. A Multigrid Algorithm for Nonlinear Monotone Elliptic Problems Rodolfo Bermejo Juan-Anton... more Page 1. A Multigrid Algorithm for Nonlinear Monotone Elliptic Problems Rodolfo Bermejo Juan-Antonio Infantey Abstract: We introduce a FAS multigrid algorithm to nd the nite element solution for a class of nonlinear monotone elliptic problems. ...
International Journal for Numerical Methods in Fluids
ABSTRACT
We present in this paper a numerical study of long-term calculations of an idealized mid-latitude... more We present in this paper a numerical study of long-term calculations of an idealized mid-latitude ocean circulation model. The objective of this paper is twofold. First, we present an efficient semi-Lagrangia scheme for eddy resolving ocean circulation models, and second, we use the so called proper orthogonal decomposition technique to characterize the finite dimensional manifold that contains the attractor of the solution. Using a Galerkin projection on this man-ifold we reduce the high dimensional system obtained by the application of the finite element method, to a low-dimensional one and , thus, we can calculate the bifurcation diagram with the horizontal eddy viscosity coefficient as a control parameter.
Communications in Computational Physics
International Journal of Numerical Analysis and Modeling
International Journal for Numerical Methods in Fluids, 2000
An algorithm based on the finite element modified method of characteristics (FEMMC) is presented ... more An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection-diffusion, Burgers and unsteady incompressible Navier-Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier-Stokes equations, an approach that
Numerical Mathematics and Advanced Applications, 2006
ABSTRACT It is well know the importance of bifurcation diagrams in fluid models where any of the ... more ABSTRACT It is well know the importance of bifurcation diagrams in fluid models where any of the parameters has some kind of uncertainty (usually the Reynolds number in Navier-Stokes, or the Ekman parameter in geophysical models). In this work we propose some modifications to the Proper Orthogonal Decomposition (POD) method (or. Karhunen-Loeve expansions) in order to study this problem. Although some of this modifications have already been introduced in the literature, most of them are devoted to computing the first Hopf bifurcation. We show here how one can handle the bifurcation diagram also in periodic branches.
Mathematical and Computer Modelling, 2009
The purpose of this paper is to carry out the mathematical and numerical analysis of a two-dimens... more The purpose of this paper is to carry out the mathematical and numerical analysis of a two-dimensional nonlinear parabolic problem on a compact Riemannian manifold without boundary, which arises in the energy balance for the averaged surface temperature. We use a possibly quasi-linear diffusion operator suggested by P.H. Stone in 1972. The modelling of the Budyko discontinuous coalbedo is formulated in terms of a bounded maximal monotone graph of R 2 . The existence of global solutions is proved by applying a fixed point argument. Since the uniqueness of solutions may fail for the case of discontinuous coalbedo, we introduce the notion of non-degenerate solutions and show that the problem has at most one solution in this class of functions. The numerical analysis is carried out for the special case of a spherical Earth and uses quasi-uniform spherical triangles as finite elements. We study the existence, uniqueness and stability of the approximate solutions. We also show results of some long-term numerical experiments.
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Papers by Rodolfo Bermejo