Rodolfo Bermejo

A Multigrid Algorithm for the p -Laplacian

We introduce a full approximation storage (FAS) multigrid algorithm to find the finite element solution for a class of nonlinear monotone elliptic problems. Since the solution of the problem is equivalent to minimize a strictly convex functional, we use a Polak--Ribiere conjugate gradient method as the nonlinear smoother in our algorithm. The advantage in so doing is that we do not have to calculate derivatives of operators. We prove local convergence of our algorithm and illustrate its performance by solving benchmark problems.

A Second Order in Time Modified Lagrange--Galerkin Finite Element Method for the Incompressible Navier--Stokes Equations

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

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

P2/P1

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

Taylor--Hood element are used.

Anisotropic “Goal-Oriented” Mesh Adaptivity for Elliptic Problems

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

Error estimates of proper orthogonal decomposition eigenvectors and Galerkin projection for a general dynamical system arising in fluid models

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

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

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

Error Analysis for hp-FEM Semi-Lagrangian Second Order BDF Method for Convection-Dominated Diffusion Problems

J(u)

Modified Lagrange--Galerkin Methods to Integrate Time Dependent Incompressible Navier--Stokes Equations

. 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

A Stochastic Semi‐Lagrangian Micro‐Macro Model for Liquid Crystalline Solutions

I:=(0,T]