Tim Wildey

A Posteriori Analysis and Improved Accuracy for an Operator Decomposition Solution of a Conjugate Heat Transfer Problem

We consider the accuracy of an operator decomposition finite element method for a conjugate heat transfer problem consisting of two materials coupled through a common boundary. We derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the differences between the adjoints of the full problem and the discrete iterative system. We use these estimates to guide adaptive mesh refinement. In addition, we address a loss of order of convergence that results from the decomposition and show that the order of convergence is limited by the accuracy of the transferred gradient information. We employ a boundary flux recovery method to regain the expected order of accuracy in an efficient manner.

A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid-solid heat transfer

We analyze a multiscale operator decomposition finite element method for a conjugate heat transfer problem consisting of a fluid and a solid coupled through a common boundary. We derive accurate a posteriori error estimates that account for all sources of error, and in particular the transfer of error between fluid and solid domains. We use these estimates to guide adaptive mesh refinement. In addition, we provide compelling numerical evidence that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information, and adapt a so-called boundary flux recovery method developed for elliptic problems in order to regain the optimal order of accuracy in an efficient manner. In an appendix, we provide an argument that explains the numerical results provided sufficient smoothness is assumed.

DOMAIN DECOMPOSITION FOR POROELASTICITY AND ELASTICITY WITH DG JUMPS AND MORTARS

We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme.

Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling

We consider discretizations of a model elliptic problem by means of different numerical methods applied separately in different subdomains, termed multinumerics, coupled using the mortar technique. The grids need not match along the interfaces. We are also interested in the multiscale setting, where the subdomains are partitioned by a mesh of size

A posteriori error analysis of multiscale operator decomposition methods for multiphysics models

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Approaches for Adjoint-Based A Posteriori Analysis of Stabilized Finite Element Methods

, whereas the interfaces are partitioned by a mesh of much coarser size

A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators

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Efficient algorithms for multiscale modeling in porous media

, and where lower-order polynomials are used in the subdomains and higher-order polynomials are used on the mortar interface mesh. We derive several fully computable a posteriori error estimates which deliver a guaranteed upper bound on the error measured in the energy norm. Our estimates are also locally efficient and one of them is robust with respect to the ratio

Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems

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Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics.

under an assumption of sufficient regularity of the weak solution. The present approach allows bounding separately and comparing mutually the subdomain and interface errors. A subdomain/interface adaptive refinement s...