Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations
From MaRDI portal
Publication:3614825
DOI10.1137/060670468zbMath1169.65098OpenAlexW1998967184MaRDI QIDQ3614825
Publication date: 10 March 2009
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/060670468
numerical experimentsadaptive algorithmparabolic equationsmesh refinementa posteriori error estimationspace-time finite elementsdynamic meshes
Nonlinear parabolic equations (35K55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)
Related Items
Error estimation and adaptivity for differential equations with multiple scales in time ⋮ Efficient Model Predictive Control for Parabolic PDEs with Goal Oriented Error Estimation ⋮ Output error estimation strategies for discontinuous Galerkin discretizations of unsteady convection-dominated flows ⋮ Space adaptive finite element methods for dynamic Signorini problems ⋮ Galerkin optimal control ⋮ A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints ⋮ A hybridized discontinuous Galerkin method on mapped deforming domains ⋮ NTFA-enabled goal-oriented adaptive space-time finite elements for micro-heterogeneous elastoplasticity problems ⋮ Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains ⋮ An adaptive Galerkin method for the time-dependent complex Schrödinger equation ⋮ Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity ⋮ Adaptive time-step control for a monolithic multirate scheme coupling the heat and wave equation ⋮ Model Reduction by Adaptive Discretization in Optimal Control ⋮ Output-based error estimation and mesh adaptation for unsteady turbulent flow simulations ⋮ Unnamed Item ⋮ Output-based space-time mesh optimization for unsteady flows using continuous-in-time adjoints ⋮ Goal-oriented adaptive refinement for phase field modeling with finite elements ⋮ Dual-based adaptive FEM for inelastic problems with standard FE implementations ⋮ A cost-efficient space-time adaptive algorithm for coupled flow and transport ⋮ Numerical modeling and open-source implementation of variational partition-of-unity localizations of space-time dual-weighted residual estimators for parabolic problems ⋮ Derivation of third order Runge-Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation ⋮ Goal-oriented a posteriori error estimation for Dirichlet boundary control problems ⋮ Tensor-product space-time goal-oriented error control and adaptivity with partition-of-unity dual-weighted residuals for nonstationary flow problems ⋮ Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems ⋮ Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods ⋮ Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation ⋮ Efficient numerical realization of discontinuous Galerkin methods for temporal discretization of parabolic problems ⋮ Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods ⋮ An anisotropic, fully adaptive algorithm for the solution of convection-dominated equations with semi-Lagrangian schemes ⋮ Adaptive time-step control for nonlinear fluid-structure interaction ⋮ An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization ⋮ Variational localizations of the dual weighted residual estimator ⋮ A posteriori error estimation for the fractional step theta discretization of the incompressible Navier-Stokes equations ⋮ On asymptotic global error estimation and control of finite difference solutions for semilinear parabolic equations ⋮ An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem ⋮ Explicit-in-time goal-oriented adaptivity ⋮ Discrete maximal parabolic regularity for Galerkin finite element methods ⋮ Estimates for the difference between exact and approximate solutions of parabolic equations on the basis of Poincaré inequalities for traces of functions on the boundary ⋮ Goal-oriented mesh adaptation for flux-limited approximations to steady hyperbolic problems ⋮ Adaptive Finite Element Methods for Parameter Identification Problems ⋮ Output-based space-time mesh adaptation for the compressible Navier-Stokes equations ⋮ Towards adjoint-based mesh refinement for large eddy simulation using reduced-order primal solutions: preliminary 1D Burgers study ⋮ Adaptive finite element discretization in PDE-based optimization ⋮ Flexible goal-oriented adaptivity for higher-order space-time discretizations of transport problems with coupled flow ⋮ Goal-oriented a posteriori error estimates for transport problems ⋮ A Posteriori Error Estimation and Adaptivity for Nonlinear Parabolic Equations using IMEX-Galerkin Discretization of Primal and Dual Equations ⋮ Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition ⋮ Pointwise Best Approximation Results for Galerkin Finite Element Solutions of Parabolic Problems ⋮ Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations ⋮ Model adaptivity on effective elastic properties coupled with adaptive FEM ⋮ Time-domain goal-oriented adaptivity using pseudo-dual error representations ⋮ Duality based error estimation in the presence of discontinuities ⋮ A Posteriori Error Estimation in PDE-constrained Optimization with Pointwise Inequality Constraints ⋮ New low order Runge-Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction
This page was built for publication: Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations
