High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations

DOI10.1007/BF01989753zbMath0802.65099MaRDI QIDQ688638

Joseph E. Flaherty, Peter K. Moore

Publication date: 30 November 1993

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergenceadaptive mesh refinementerror estimationGalerkin's methodcomputational resultssingly implicit Runge-Kutta methodsfinite element method-of-lines

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 (7)

Comparison of adaptive methods for one-dimensional parabolic systems ⋮ Integrated space-time adaptive \(hp\)-refinement methods for parabolic systems ⋮ A COMPLETE ANALYSIS FOR SOMEA POSTERIORIERROR ESTIMATES WITH THE FINITE ELEMENT METHOD OF LINES FOR A NONLINEAR PARABOLIC EQUATION ⋮ Fully discrete error estimation by the method of lines for a nonlinear parabolic problem. ⋮ Modeling and the adaptive solution of CVD fiber-coating process ⋮ Error estimates and adaptive finite element methods ⋮ Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation

Uses Software

• RODAS

Cites Work

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• Moving finite element methods for evolutionary problems. II: Applications
• A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
• Galerkin/Runge–Kutta Discretizations for Semilinear Parabolic Equations
• A Transformed implicit Runge-Kutta Method
• An implementation of singly-implicit Runge-Kutta methods
• A special family of Runge-Kutta methods for solving stiff differential equations
• 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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