相关论文: Low regularity integrators for semilinear paraboli…
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has…
In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
For the time-fractional phase field models, the corresponding energy dissipation law has not been settled on both the continuous level and the discrete level. In this work, we shall address this open issue. More precisely, we prove for the…
We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regularisation viewpoint of the wave equation in second-order…
In this article, we present the existence, uniqueness, and regularity of solutions to parabolic equations with non-local operators $$ \partial_{t}u(t,x) = \mathcal{L}^{a}u(t,x) + f(t,x), \quad t>0 $$ in $L_{q}(L_{p})$ spaces. Our spatial…
This paper proposes a new methodology in linear time-periodic (LTP) system identification. In contrast to previous methods that totally separate dynamics at different tag times for identification, the method focuses on imposing appropriate…
In this paper, we propose and analyze a time-stepping method for the time fractional Allen-Cahn equation. The key property of the proposed method is its unconditional stability for general meshes, including the graded mesh commonly used for…
The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
We study the stability of a class of dynamical low-rank methods--the projector-splitting integrator (PSI)--applied to linear hyperbolic and parabolic equations. Using a von Neumann-type analysis, we investigate the stability of such…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…
The blue phases are fascinating and complex states of chiral liquid crystals which can be modeled by a comprehensive framework of the Landau-de theory, satisfying energy dissipation and maximum bound principle. In this paper, we develop and…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
This paper presents a class of Crank-Nicolson (CN) type schemes enhanced by radial basis function (RBF) interpolation for the time integration of linear parabolic partial differential equations (PDEs). The resulting RBF-CN schemes preserve…