The p- and h-p version of the finite element method, an overview
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Parallel computation of flow in heterogeneous media modelled by mixed finite elements
Journal of Computational Physics
Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB
Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB
Automatic Mesh Generation: Applications to Finite Element Methods
Automatic Mesh Generation: Applications to Finite Element Methods
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Parallel adaptive time domain decomposition for stiff systems of ODEs/DAEs
Computers and Structures
Convergence analysis of optimization-based domain decomposition methods for a bonded structure
Applied Numerical Mathematics
A posteriori error analysis of a domain decomposition algorithm for unilateral contact problem
Computers and Structures
Stochastic structural dynamic analysis using Bayesian emulators
Computers and Structures
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A complex system can be modeled using various fidelities with the finite element method. A high-fidelity model is expected to be more computationally expensive compared to a low-fidelity model and in general may contain more degrees of freedom and more elements. This paper proposes a novel multi-fidelity approach to solve boundary value problems using the finite element method. A Bayesian approach based on Gaussian process emulators in conjunction with the domain decomposition method is developed. Using this approach one can seamlessly assimilate a low-fidelity model with a more expensive high-fidelity model. The idea is illustrated using elliptic boundary value problems.