High-order discretisations and efficient direct space-time finite element solvers for parabolic initial-boundary value problems

DOI10.1007/978-3-031-20432-6_37MaRDI QIDQ6620252

Marco Zank

Publication date: 16 October 2024

zbMATH Keywords

heat equationspace-time finite element solvers

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for matrix equations (65F45)

Cites Work

• A survey on direct solvers for Galerkin methods
• Coercive space-time finite element methods for initial boundary value problems
• A note on the efficient evaluation of a modified Hilbert transformation
• An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations
• Computational Methods for Linear Matrix Equations
• Initial-Boundary Value Problems for Parabolic Equations
• Solution of the Sylvester matrix equation AXB ^T + CXD ^T = E
• Finite Elements I
• Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces
• Fast Direct Solvers for Elliptic PDEs
• Parallel and Robust Preconditioning for Space-Time Isogeometric Analysis of Parabolic Evolution Problems
• Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
• Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2

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