Integrated space-time adaptive \(hp\)-refinement methods for parabolic systems

DOI10.1016/0168-9274(94)00059-PzbMath0818.65089MaRDI QIDQ1347140

Joseph E. Flaherty, Peter K. Moore

Publication date: 22 August 1995

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceerror estimatesnumerical examplesparabolic systemsgrid prediction strategysingly implicit Runge-Kutta stagesspace-time adaptive \(hp\)-refinement strategies

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (16)

Dynamical \(p\)-adaptivity for LES of compressible flows in a high order DG framework ⋮ An adaptive moving mesh method with static rezoning for partial differential equations ⋮ Comparison of adaptive methods for one-dimensional parabolic systems ⋮ An implicit interpolation error-based error estimation strategy for hp-adaptivity in one space dimension ⋮ A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method ⋮ A fully adaptive MOL-treatment of parabolic 1-D problems with extrapolation techniques ⋮ Adaptive FEM for reaction-diffusion equations ⋮ Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions ⋮ A locally \(p\)-adaptive approach for large eddy simulation of compressible flows in a DG framework ⋮ Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps. ⋮ Parameter estimation in one-dimensional time-dependet partial differential equations ⋮ The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions ⋮ Comparison of hp-adaptive error estimates for second order hyperbolic systems ⋮ Avoiding spurious modes of time discretized operators in transport problems ⋮ An adaptive finite element method for magnetohydrodynamics ⋮ Error estimates and adaptive finite element methods

Cites Work

• High-order adaptive methods for parabolic systems
• High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations
• The finite element method for parabolic equations. II. A posteriori error estimation and adaptive approach
• Mesh design for the p-version of the finite element method
• A moving-mesh finite element method with local refinement for parabolic partial differential equations
• Moving finite element methods for evolutionary problems. II: Applications
• A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
• The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• A Transformed implicit Runge-Kutta Method
• An implementation of singly-implicit Runge-Kutta methods
• Runge-Kutta methods with a multiple real eigenvalue only
• A special family of Runge-Kutta methods for solving stiff differential equations
• A Posteriori Error Estimation with Finite Element Semi- and Fully Discrete Methods for Nonlinear Parabolic Equations in One Space Dimension
• Balancing Space and Time Errors in the Method of Lines for Parabolic Equations
• A Local Refinement Finite-Element Method for One-Dimensional Parabolic Systems
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