Name
Title | ||
|---|---|---|
Optimal order a posteriori error estimates for a class of Runge–Kutta and Galerkin methods |
Abstract | ||
|---|---|---|
We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximate solutions and pointwise error representations. The reconstructions are based on rather general orthogonality properties and lead to upper and lower bounds for the error regardless of the time-step; they do not hinge on asymptotics. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s00211-009-0254-2 | Numerische Mathematik |
Keywords | Field | DocType |
galerkin method,continuous galerkin method,general orthogonality property,a posteriori error analysis,parabolic equations.,time reconstruction,kutta collocation,appropriate one-degree,exhibit optimal global order,key ingredient,posteriori error estimate,approximate solution,continuous reconstruction,optimal order,continuous galerkin,. runge-kutta methods,pointwise error representation,collocation methods,runge kutta method,parabolic equation,collocation method,runge kutta,upper and lower bounds | Runge–Kutta methods,Mathematical optimization,Mathematical analysis,Upper and lower bounds,Galerkin method,Optimal estimation,Partial differential equation,Mathematics,Parabola,Collocation,Pointwise | Journal |
Volume | Issue | ISSN |
114 | 1 | 0945-3245 |
Citations | PageRank | References |
10 | 1.06 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Georgios Akrivis | 1 | 158 | 32.43 |
| Charalambos Makridakis | 2 | 253 | 48.36 |
| Ricardo H. Nochetto | 3 | 907 | 110.08 |