A Space-Time Multiscale Method for Parabolic Problems

Space-time Domain Decomposition for Parabolic Problems Space-time Domain Decomposition for Parabolic Problems

We analyze a space-time domain decomposition iteration, for a model advection diiusion equation in one and two dimensions. The asymptotic convergence rate is superlinear, and it is governed by the diiusion of the error across the overlap between subdomains. Hence, it depends on both the size of this overlap and the diiusion coeecient in the equation. However, it is independent of the number of ...

Linearized Numerical Homogenization Method for Nonlinear Monotone Parabolic Multiscale Problems

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the m...

Linerarized numerical homogenization method for nonlinear monotone parabolic multiscale problems

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the m...

Analysis of the heterogeneous multiscale method for parabolic homogenization problems

The heterogeneous multiscale method (HMM) is applied to various parabolic problems with multiscale coefficients. These problems can be either linear or nonlinear. Optimal estimates are proved for the error between the HMM solution and the homogenized solution.

Multiscale Realization and Estimation for Space and Space-Time Problems