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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1007/s00198-010-1395-y

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0945-3245

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Galerkin and Runge–Kutta methods unified formulat

Authors: Georgios Akrivis Charalambos Makridakis Ricardo H Nochetto
Publish Date: 2011/02/25
Volume: 118, Issue: 3, Pages: 429-456
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Abstract

We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations This together with the concept of reconstruction of the approximate solutions allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methodsGeorgios Akrivis was partially supported by the Institute of Applied and Computational Mathematics FORTH Greece Charalambos Makridakis was partially supported by the RTNnetwork HYKE HPRNCT200200282 the EU Marie Curie Dev Host Site HPMDCT200100121 and the program Pythagoras of EPEAEK II Ricardo H Nochetto was partially supported by NSF grants DMS0505454 and DMS0807811

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  1. Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
  2. A new class of symplectic integration schemes based on generating functions
  3. An optimal adaptive finite element method for elastoplasticity
  4. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain
  5. Decay rates of adaptive finite elements with Dörfler marking
  6. Multi-parameter regularization and its numerical realization
  7. Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
  8. Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
  9. A uniformly stable Fortin operator for the Taylor–Hood element
  10. A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses
  11. Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
  12. The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
  13. Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
  14. Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization
  15. Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods
  16. A residual–based error estimator for BEM–discretizations of contact problems
  17. An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems
  18. Preconditioners for pseudodifferential equations on the sphere with radial basis functions
  19. Symmetric multistep methods for constrained Hamiltonian systems
  20. Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations
  21. Numerical Eulerian method for linearized gas dynamics in the high frequency regime
  22. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
  23. The boundary element spline collocation for nonuniform meshes on the torus
  24. Delay-dependent stability of high order Runge–Kutta methods
  25. Intrinsic finite element methods for the computation of fluxes for Poisson’s equation
  26. On generalized successive overrelaxation methods for augmented linear systems
  27. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
  28. A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
  29. Intrinsic representation of tangent vectors and vector transports on matrix manifolds
  30. Crouzeix–Raviart boundary elements
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