667 research outputs found
A posteriori error control for discontinuous Galerkin methods for parabolic problems
We derive energy-norm a posteriori error bounds for an Euler time-stepping
method combined with various spatial discontinuous Galerkin schemes for linear
parabolic problems. For accessibility, we address first the spatially
semidiscrete case, and then move to the fully discrete scheme by introducing
the implicit Euler time-stepping. All results are presented in an abstract
setting and then illustrated with particular applications. This enables the
error bounds to hold for a variety of discontinuous Galerkin methods, provided
that energy-norm a posteriori error bounds for the corresponding elliptic
problem are available. To illustrate the method, we apply it to the interior
penalty discontinuous Galerkin method, which requires the derivation of novel a
posteriori error bounds. For the analysis of the time-dependent problems we use
the elliptic reconstruction technique and we deal with the nonconforming part
of the error by deriving appropriate computable a posteriori bounds for it.Comment: 6 figure
Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints
Finite element methods for a model elliptic distributed optimal control
problem with pointwise state constraints are considered from the perspective of
fourth order boundary value problems
Discontinuous Galerkin Methods for an Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints
We investigate discontinuous Galerkin methods for an elliptic optimal control
problem with a general state equation and pointwise state constraints on
general polygonal domains. We show that discontinuous Galerkin methods for
general second-order elliptic boundary value problems can be used to solve the
elliptic optimal control problems with pointwise state constraints. We
establish concrete error estimates and numerical experiments are shown to
support the theoretical results
hp-Version discontinuous Galerkin finite element methods for semilinear parabolic problems
We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp--DGFEM on shape--regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non--symmetric versions of DGFEM
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