Slow slip events on tectonic faults, sliding instabilities that never accelerate to inertially limited ruptures or earthquakes, are one of the most enigmatic phenomena in frictional sliding. While observations of slow slip events continue to mount, a plausible mechanism that permits instability while simultaneously limiting slip speed remains elusive. Rate-andstate friction has been successful in describing most aspects of rock friction, faulting, and earthquakes; current explanations of slow slip events appeal to rate-weakening friction to induce instabilities, which are then stalled by additional stabilizing processes like dilatancy or a transition to rate-strengthening friction at high slip rates. However, the temperatures and/or clay-rich compositions at slow slip locations are almost ubiquitously associated with rate-strengthening friction. In this study, we propose a fundamentally different instability mechanism that may reconcile this contradiction, demonstrating how slow slip events can nucleate with mildly rate-strengthening friction. We identify two destabilizing mechanisms, both reducing frictional shear strength through reductions in effective normal stress, that counteract the stabilizing effects of rate-strengthening friction. The instability develops into slow slip pulses. We quantify parameter controls on pulse length, propagation speed, and other characteristics, and demonstrate broad consistency with observations of tectonic slow slip events as well as laboratory tribology experiments.

Optimal boundary closures are derived for first derivative, finite difference operators of order 2, 4, 6 and 8. The closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids and entropy stability for nonlinear equations that support a convex extension. The new closures are developed by enriching conventional approaches with additional boundary closure stencils and non-equidistant grid distributions at the domain boundaries. Greatly improved accuracy is achieved near the boundaries, as compared with traditional diagonal norm operators of the same order. The superior accuracy of the new optimal diagonal-norm SBP operators is demonstrated for linear hyperbolic systems in one dimension and for the nonlinear compressible Euler equations in two dimensions.

We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the non-conforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces.

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