Space-time Finite Element Analysis of Advection-Diffusion Equation with Galerkin/Least-Square Stabilization
Belangrijkste concepten
Full space-time numerical solution of advection-diffusion equation using Galerkin/least-square method.
Samenvatting
The content discusses the application of the Galerkin/least-square method to ensure stability in solving the advection-diffusion equation. It explores a full space-time formulation, providing error estimates and demonstrating convergence with numerical examples. The article also delves into adaptive space-time mesh refinement for efficient solutions.
Structure:
Introduction to transient problem discretization methods.
Space-time formulation as an alternative strategy.
Historical context and interest in space-time formulations by the finite element community.
Stability analysis of discrete space-time formulation using Galerkin/least squares approach.
Reduction of computational cost through adaptive space-time mesh refinement.
Mathematical formulation details for time-dependent linear advection-diffusion equation.
Discrete variational problem definition and solution approach.
Stability and convergence analysis of stabilized formulations.
Numerical examples showcasing convergence studies and comparison between sequential and space-time solutions.
Adaptive solutions demonstration with heat diffusion problem and advection-diffusion equation.
Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization
"The finite element community has a history of considering solutions to time dependent PDEs in space-time."
"In this work, we tackle two key aspects associated with solving evolution equations in space-time – stability and computational cost."