Related papers: Discrete maximal regularity and the finite element…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
This paper establishes the optimal $H^1$-norm error estimate for a nonstandard finite element method for approximating $H^2$ strong solutions of second order linear elliptic PDEs in non-divergence form with continuous coefficients. To…
We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…
In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms.…
The symmetric $p$-Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this work, second-order differentiability properties of solutions to…
A quantitative regularity theory is developed for weak solutions to the parabolic system $$ \partial_t u-\mathrm{div}\,{\boldsymbol{\mathsf A}}(x,t,Du)=0 \quad\text{in }E_T\subset \mathbb{R}^N\times\mathbb{R}, $$ which features the…
A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and…
This paper is concerned about maximum principles and radial symmetry for viscosity solutions of fully nonlinear partial differential equations. We obtain the radial symmetry and monotonicity properties for nonnegative viscosity solutions of…
We develop an optimal regularity theory for $L^p$-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form whose gradient growth is described through a Hamiltonian function with measurable and possibly…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n. Well-posedness of solutions reconstructing maximal parabolic regularity in nonlinear thermoelastic plates is…
This paper presents a modified quasi-reversibility method for computing the exponentially unstable solution of a nonlocal terminal-boundary value parabolic problem with noisy data. Based on data measurements, we perturb the problem by the…
In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the…
In this paper we produce new, optimal, regularity results for the solutions to $p$-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent $p$, that imports information from a limiting…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm…
The maximum principle forms an important qualitative property of second order elliptic equations, therefore its discrete analogues, the so-called discrete maximum principles (DMPs) have drawn much attention. In this paper DMPs are…
We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In…