Jaime Carpio

A Space-Time Adaptive Finite Element Algorithm Based on Dual Weighted Residual Methodology for Parabolic Equations

We propose in this paper a space-time adaptive algorithm based on the dual weighted residual (DWR) idea in the framework of a finite element method. Our algorithm consists of applying the DWR technique locally in each time interval

Mathematical and numerical analysis of a nonlinear diffusive climate energy balance model

I_n:=(t_{n-1},t_n]

Anisotropic “Goal-Oriented” Mesh Adaptivity for Elliptic Problems

, and thus, we control the local or truncation error for a functional of the solution

A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

J(u)

Multivariate Exponential Smoothing and Dynamic Factor Model Applied to Hourly Electricity Price Analysis

. The disadvantage of our method compared to the traditional DWR method is that having a good local error control does not guarantee that the global error will be bounded. However, the main advantage of our method is that we avoid solving backward in the whole time interval

Diffusion-flame flickering as a hydrodynamic global mode

I:=(0,T]

A-SLEIPNNIR: A multiscale, anisotropic adaptive, particle level set framework for moving interfaces. Transport equation applications

the associated linear dual problem so that the storage requirements are smaller. This means that we can define a self-sufficient criterion that allows us to have control of the time step

EM estimation of multivariate dynamic models for predicting electricity prices

\Delta t

An approach to operational modal analysis using the expectation maximization algorithm

and the mesh size h as time of integration progresses. Another good feature of our algorithm is the extension of the spatial postprocessing procedure of the traditional DWR method to unstructu...

Critical radius for hot-jet ignition of hydrogen-air mixtures

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.