Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal order FEM for dynamic poroelasticity: Error analysis for equal order elements

Markus Bause, Mathias Anselmann

Abstract

The numerical approximation of dynamic poroelasticity, modeling flow in deformable porous media, by a family of continuous space-time finite element methods is investigated. Equal order approximation in space without any further stabilization is used for the displacement and pore pressure variable. Optimal order $L^\infty(L^2)$ error estimates are proved and numerically confirmed.

Optimal order FEM for dynamic poroelasticity: Error analysis for equal order elements

Abstract

The numerical approximation of dynamic poroelasticity, modeling flow in deformable porous media, by a family of continuous space-time finite element methods is investigated. Equal order approximation in space without any further stabilization is used for the displacement and pore pressure variable. Optimal order error estimates are proved and numerically confirmed.
Paper Structure (6 sections, 2 theorems, 27 equations, 2 tables)

This paper contains 6 sections, 2 theorems, 27 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Numerical scheme
  3. Error estimation
  4. Proof
  5. Proof
  6. Numerical convergence study

Key Result

Theorem 3.1

For the approximation $(\boldsymbol u_{\tau,h},\boldsymbol v_{\tau,h},p_{\tau,h})$ defined by Problem Prob:CG of the sufficiently regular solution $(\boldsymbol u,\boldsymbol v, p)$ to Eq:HPS and a suitable choice of the discrete initial values $(\boldsymbol u_{0,h},\boldsymbol v_{0,h}, p_{0,h})\in

Theorems & Definitions (4)

  • Theorem 3.1: Error estimate
  • Definition 3.2: Special approximation $(\boldsymbol w_1,\boldsymbol w_2)$ of $(\boldsymbol u, \partial_t \boldsymbol u)$
  • Lemma 3.3: Improved order estimation of $\partial_t \boldsymbol \eta_1$
  • Remark 3.4