Mixed finite elements for second order elliptic problems in three variables
Numerische Mathematik
Stability and convergence at the PDE/stiff ODE interface
Applied Numerical Mathematics - Recent Theoretical Results in Numerical Ordinary Differential Equations
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Difference schemes with domain decomposition for solving non-stationary problems
USSR Computational Mathematics and Mathematical Physics
Journal of Computational Physics
Interior estimates for time discretizations of parabolic equations
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
Domain Decomposition Operator Splittings for the Solution of Parabolic Equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems
Mathematics of Computation
Fractional step Runge--Kutta methods for time dependent coefficient parabolic problems
Applied Numerical Mathematics
Quadrilateral H(div) Finite Elements
SIAM Journal on Numerical Analysis
Robust convergence of multi point flux approximation on rough grids
Numerische Mathematik
A Multipoint Flux Mixed Finite Element Method
SIAM Journal on Numerical Analysis
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations (Lecture Notes in Computational Science and Engineering)
Local flux mimetic finite difference methods
Numerische Mathematik
Some remarks on quadrilateral mixed finite elements
Computers and Structures
A generalization of Peaceman-Rachford fractional step method
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media
Journal of Computational Physics
A Multipoint Flux Mixed Finite Element Method on Hexahedra
SIAM Journal on Numerical Analysis
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Numerische Mathematik
Hi-index | 31.45 |
We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge-Kutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.