In this paper, we investigate a residual-based posteriori error estimates for the hp finite element approximation of general optimal control problems governed by bilinear elliptic equations. By using the hp discontinuous Galerkin finite element approximation for the control and the hp finite element approximation for both the state and the co-state, we derive a posteriori upper error bounds for...

Abstract. The two common approaches to defining coarse operators in multigrid numerical algorithms are discretization coarse approximation (DCA) and (Petrov-)Galerkin coarse approximation (GCA). Here, a new approach called collocation coarse approximation (CCA) is introduced, which—like GCA—is algebraically defined and able to cater to difficult features such as discontinuous coefficients, but,...

Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochastic) inputs. We consider the related problem of a matrix equation whose matrix and right-hand side depend on a set of parameters (e.g., a PDE with stochastic inputs semidiscretized in space) and examine the linear syst...

We present an extension of the Generalized Spectral Decomposition method for the resolution of non-linear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multiwavelets). Two algorithms are proposed for the sequential c...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

A new approach to the numerical solution of systems of first-order ordinary differential equations is given by finding local Galerkin approximations on each subinterval of a given mesh of size h. One step at a time, a piecewise polynomial, of degree n and class C°, is constructed, which yields an approximation of order 0(A*") at the mesh points and 0(A"+1) between mesh points. In addition, the ...