Browsing Department of Mathematics by Journals "Computers and Mathematics with Applications"
Now showing items 1-6 of 6
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An adaptive solution strategy for Richards' equation
(Journal article; Peer reviewed, 2023)Flow in variably saturated porous media is typically modeled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and ... -
Convergence of a continuous Galerkin method for hyperbolic-parabolic systems
(Journal article; Peer reviewed, 2024)We study the numerical approximation by space-time finite element methods of a coupled hyperbolic-parabolic system modeling, for instance, poro- and thermoelasticity. The equations are rewritten as a first-order system in ... -
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
(Journal article; Peer reviewed, 2021)The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing ... -
Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
(Journal article; Peer reviewed, 2020)This paper concerns monolithic and splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulated as a three-field system ... -
A robust solution strategy for the Cahn-Larché equations
(Journal article; Peer reviewed, 2023)In this paper we propose a solution strategy for the Cahn-Larché equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. ... -
Splitting schemes for coupled differential equations: Block Schur-based approaches & Partial Jacobi approximation[Formula presented]
(Journal article; Peer reviewed, 2024)Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. In a broad sense, one can categorise the numerical solution strategies for coupled problems into two ...