Multilevel Adaptive Particle Methods for Convection-Diffusion Equations

Multilevel Adaptive Particle Methods for Convection-Diffusion Equations

We present novel multilevel particle methods with extended adaptivity in areas where increased resolution is required. We present two complementary approaches as inspired by r-adaptivity and adaptive mesh refinement (AMR) concepts introduced in finite difference and finite element schemes. For the r-adaptivity a new class of particle based mapping functions is introduced while the particle-AMR ...

Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations

Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis methods is a suitable means to reduce computational time. In this proceedings, we show the applicability of the reduced basis framew...

Adaptive Discontinuous Galerkin Methods for Nonlinear Diffusion-Convection-Reaction Equations

In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion convection reaction equations. We propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non-linear equations. Numerical examples demonstrate effectiveness of the DG...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Multilevel Adaptive Methods for Semilinear Equations